Google Sheets, 83 81 bytes

=ArrayFormula(JOIN("+",TRIM(TEXT(A:A/B:B,"?/???")))&"="&TEXT(sum(A:A/B:B),"?/???"

_{^{Saved 2 bytes thanks to Taylor Scott}}

Sheets will automatically add 2 closing parentheses to the end of the formula.

The two arrays are input as the entirety of columns A and B. Empty rows below the inputs will throws errors.

Haskell (Lambdabot), 94 91 86 bytes

t=tail.(([n,_,d]->'+':n++'/':d).words.show=<<)
a#b|f<-zipWith(%)a b=t f++'=':t[sum f]

Try it online!

Thanks @Laikoni for -8 bytes!

Ungolfed

-- convert each fraction to a string (has format "n%d", replace '%' with '/' and prepend '+' ("+n/d"), keep the tail (dropping the leading '+')
t = tail.(([n,_,d]->'+':n++'/':d).words.show=<<)
-- build a list of fractions
a # b = let f = zipWith(%) a b in
-- stringify that list, append "=" and the stringified sum of these fractions
  t f ++ "=" ++ t [sum f]

Casio Basic, 161 Bytes

Dim(List 1)->A
for 1->I to A step 1
3*I-2->B
List 1[I]->C
List 2[I]->D
locate 1,B,C
locate 1,B+1,"/"
locate 1,B+2,D
C/D+E->E
next
locate 1,B+3,"="
locate 1,B+4,E

Explanation:

• Number of input is saved in A
• A iterations
• B acts as a counter for correct displaying
• I'th item of List 1 and 2 saved in C and D
• Displaying of Variable C / Variable D
• save C/D+E in E
• After last number locate = and E

Axiom, 212 bytes

C==>concat;S==>String;g(a)==C[numerator(a)::S,"/",denom(a)::S];h(a:List PI,b:List PI):S==(r:="";s:=0/1;#a~=#b or #a=0=>"-1";for i in 1..#a repeat(v:=a.i/b.i;s:=s+v;r:=C[r,g(v),if i=#a then C("=",g(s))else"+"]);r)

test

(5) -> h([1,3,4,4,5,6], [2,9,5,5,6,7])
   (5)  "1/2+1/3+4/5+4/5+5/6+6/7=433/105"
                                                             Type: String
(6) -> h([1,3,4,4], [2,9,5,5,6,7])
   (6)  "-1"
                                                             Type: String

setlX, 62 bytes

[a,b]|->join([x/y:[x,y]in a><b],"+")+"="++/[x/y:[x,y]in a><b];

ungolfed:

[a,b]|->                  define a function with parameters a and b
  join(                 
    [ x/y :               using set comprehension, make a list of fractions 
      [x,y] in a><b       from the lists zipped together
    ],
    "+"
  )                       join them with "+"
  + "="                   concat with an equals sign
  +                       concat with
  +/[x/y:[x,y]in a><b]    the sum of the list
;

setlX, 103 bytes

f:=procedure(a,b){i:=1;l:=[];while(i<=#a){l:=l+[a[i]/b[i]];i+=1;}s:=join(l,"+");return s+"="+eval(s);};

Creates a function called f where your insert two lists.

ungolfed:

f := procedure (a,b) {
    i:=1;
    l:=[];
    while(i<=#a){
        l:=l+[a[i]/b[i]];
        i+=1;
    }
    s:=join(l,"+");
    return s+"="+eval(s);
};

with named variables and annotations:
_{setlX doesn't provide a comment feature so let's just pretend that we can comment with %}

f := procedure(firstList,secondList) {
    count := 1;
    list := []; 
    while(count <= #firstList) {
        % calculate every fraction and save it as a list
        list := list + [firstList[count]/secondList[count]];
        count += 1;
    }
    % Seperate every list entry with a plus ([2/3,1] -> "2/3+1")
    str := join(list, "+");
    % eval executes the string above and thus calculates our sum
    return str + "=" + eval(str);
};

C, 171 bytes

Try Online

i;t;x;y;f(int s,int*a,int*b){x=*a;y=*b;while(++i<s)x=(y-b[i])?(x*b[i])+(a[i]*y):(x+a[i]),y=(y-b[i])?(b[i]*y):y;for(i=1;i<=(x<y?x:y);++i)t=(x%i==0&&y%i==00)?i:t;x/=t;y/=t;}

PHP>=7.1, 190 Bytes

<?function f($x,$y){for($t=1+$x;$y%--$t||$x%$t;);return$x/$t."/".$y/$t;}[$n,$d]=$_GET;for($p=array_product($d);$x=$n[+$k];$e+=$x*$p/$y)$r[]=f($x,$y=$d[+$k++]);echo join("+",$r)."=".f($e,$p);

Online Version

+14 Bytes for replacement return$x/$t."/".$y/$t; with return$y/$t>1?$x/$t."/".$y/$t:$x/$t; to output n instead of n/1

F#, 244 241 239 bytes

let rec g a=function|0->abs a|b->g b (a%b)
let h a b=g a b|>fun x->a/x,b/x
let s,n,d=List.fold2(fun(s,n,d)N D->
 let(N,D),(n,d)=h N D,h(n*D+N*d)(d*D)
 s@[sprintf"%i/%i"N D],n,d)([],0,1)nom div
printf"%s=%i/%i"(System.String.Join("+",s))n d

Try it online!

TI-BASIC, 100 bytes

:L₁⁄L₂                                              //Creates a fraction from Lists 1 & 2, 7 bytes
:toString(Ans→Str1                                  //Create string from list, 7 bytes
:inString(Ans,",→A                                  //Look for commas, 9 bytes
:While A                                            //Begin while loop, 3 bytes
:Str1                                               //Store Str1 to Ans, 3 bytes
:sub(Ans,1,A-1)+"+"+sub(Ans,A+1,length(Ans)-A→Str1  //Replace "," with "+", 33 bytes
:inString(Ans,",→A                                  //Check for more commas, 9 bytes
:End                                                //End while loop, 2 bytes
:Str1                                               //Store Str1 to Ans, 3 bytes
:sub(Ans,2,length(Ans)-2                            //Remove opening and closing brackets, 13 bytes
:Ans+"="+toString(expr(Ans                          //Add "=" and answer, 11 bytes

Note the ⁄ at the beginning, different from /. This makes the fractions hold their forms. It does work with negative fractions.

Sigh. TI-BASIC is horrible with strings. If all we had to do was print the fractions, and then their sum, the code would be:

TI-BASIC, 12 bytes

:L₁⁄L₂    //Create fractions from lists, 7 bytes
:Disp Ans //Display the above fractions, 3 bytes
:sum(Ans  //Display the answer, 2 bytes

That means that 88 bytes of my code is spent just formatting the answer! Hmph.

Julia v0.4+, 66 53 bytes

-13 bytes thanks to Dennis

a^b=replace(join(a.//b,"+")"=$(sum(a.//b))","//","/")

Try it Online!

Alternately, if fractions can be displayed using // rather than /, the following works for 35 bytes:

a^b=join(a.//b,'+')"=$(sum(a.//b))"

R, 109 bytes

f=MASS::fractions;a=attributes
g=function(n,d)paste(paste(a(f(n/d))$f,collapse='+'),a(f(sum(n/d)))$f,sep='=')

requires the MASS library (for its fractions class). the function g returns the required output as a string.

Try it online! (R-fiddle link)

Jelly, 31 bytes

,:gj”/
ṙJ$ṖP×Sç⁸P¤,ç@"j”+$¥Ṛj”=

Try it online!

MATL, 32 bytes

/YQv'%i/%i+'wYD3L)61yUYQVwV47b&h

Try at MATL online!

Explanation

Consider [1, 2, 3, 3, 6], [2, 9, 3, 2, 4] as input.

/         % Implicit inout. Divide element-wise
          % STACK: [0.5 0.222 1 1.5 1.5]
YQ        % Rational approximation (with default tolerance)
          % STACK: [1 2 1 3 3], [2 9 1 2 2]
v         % Conctenate all stack elements vertically
          % STACK: [1 2; 2 9; 1 2; 3 2; 3 2]
'%i/%i+'  % Push this string (sprintf format specifier)
          % STACK: [1 2; 2 9; 1 2; 3 2; 3 2], '%i/%i+'
wYD       % Swap, sprintf
          % STACK: '1/2+2/9+1/1+3/2+3/2+'
3L)       % Remove last entry
          % STACK: '1/2+2/9+1/1+3/2+3/2'
61        % Push 61 (ASCII for '=')
          % STACK: '1/2+2/9+1/1+3/2+3/2', 61
y         % Duplicate from below
          % STACK: '1/2+2/9+1/1+3/2+3/2', 61, '1/2+2/9+1/1+3/2+3/2'
U         % Evaluste string into a number
          % STACK: '1/2+2/9+1/1+3/2+3/2', 61, 4.722
YQ        % Rational approximation 
          % STACK: '1/2+2/9+1/1+3/2+3/2', 61, 85, 18
VwV       % Convert to string, swap, convert to string
          % STACK: '1/2+2/9+1/1+3/2+3/2', 61, '18', '85'
47        % Push 47 (ASCII for '/')
          % STACK: '1/2+2/9+1/1+3/2+3/2', 61, '18', '85', 47
b         % Bubble up in stack
          % STACK: '1/2+2/9+1/1+3/2+3/2', 61, '85', 47, '18'
&h        % Concatenate all stack elements horizontally. Implicitly display
          % STACK: '1/2+2/9+1/1+3/2+3/2=85/18'

Clojure, 71 bytes

#(let[S(map / % %2)](apply str(concat(interpose '+ S)['=(apply + S)])))

Yay for built-in fractions!

Java, 225 bytes

int c(int a,int b){return b>0?c(b,a%b):a;}
(N,D)->{int n=0,d=1,i=0,g;String s="";for(;i<N.length;g=g(N[i],D[i]),N[i]/=g,D[i]/=g,s+=(i>0?"+":"")+N[i]+"/"+D[i],n=n*D[i]+N[i]*d,d*=D[i++],g=g(n,d),n/=g,d/=g);return s+"="+n+"/"+d;}

N and D are both int[], contextualized.

I reused Kevin Cruijssen's GCD function.

See it and test it online!

Perl 6,  77  73 bytes

{join('+',($/=[@^a Z/ @^b]).map:{.nude.join('/')})~"="~$/.sum.nude.join('/')}

Try it

{($/=[@^a Z/@^b])».nude».join('/').join('+')~'='~$/.sum.nude.join('/')}

Try it

Expanded:

{  # bare block lambda with two placeholder params ｢@a｣ and ｢@b｣

  (
    $/ = [              # store as an array in ｢$/｣ for later use

      @^a Z/ @^b        # zip divide the two inputs (declares them)

    ]

  )».nude              # get list of NUmerators and DEnominators
  ».join('/')           # join the numerators and denominators with ｢/｣

  .join('+')            # join that list with ｢+｣

  ~
  '='                   # concat with ｢=｣
  ~

  $/.sum.nude.join('/') # get the result and represent as fraction
}

Perl 6, 72 bytes 65 bytes

Native and automatic rationals should make this easy, but default stringification is still as decimal, so we have to .nude (numerator and denominator) which kills our score and makes the 1 ugly :(

my n = 1,2,3,3,6; my d = 2,9,3,2,4;
(n Z/d)».nude».join("/").join("+")~"="~([+] n Z/d).nude.join("/")

Update: Removed unneeded brackets, kill more space and use smarter map. Saves characters over Brad's solution at the cost of no not being a lambda sub.

Mathematica, 33 bytes

Row@{Row[#/#2,"+"],"=",Tr[#/#2]}&

input

[{1, 2, 3, 3, 6}, {2, 9, 3, 2, 4}]

JavaScript (ES6), 111 bytes

Takes the lists in currying syntax (a)(b).

let f =

a=>b=>a.map((v,i)=>F(A=v,B=b[i],N=N*B+v*D,D*=B),N=0,D=1,F=(a,b)=>b?F(b,a%b):A/a+'/'+B/a).join`+`+'='+F(A=N,B=D)

console.log(f([1, 2, 3, 3, 6])([2, 9, 3, 2, 4]))

Ruby 2.4, 54 53 characters

->n,d{a=n.zip(d).map{|n,d|n.to_r/d};a*?++"=#{a.sum}"}

Thanks to:

• Value Ink for the Ruby 2.4 specific version (-3 characters)
• Value Ink for optimizing the Rational initialization (-1 character)

Ruby, 58 57 56 characters

->n,d{t=0;n.zip(d).map{|n,d|t+=r=n.to_r/d;r}*?++"=#{t}"}

Sample run:

irb(main):001:0> puts ->n,d{t=0;n.zip(d).map{|n,d|t+=r=n.to_r/d;r}*?++"=#{t}"}[[1, 2, 3, 3, 6], [2, 9, 3, 2, 4]]
1/2+2/9+1/1+3/2+3/2=85/18

Try it online!

Mathematica, 61 bytes

t=#~ToString~InputForm&;Riffle[t/@#,"+"]<>"="<>t@Tr@#&[#/#2]&

05AB1E, 35 34 bytes

‚øvyy¿÷'/ý'+}¨'=¹.¿©¹÷²*O®‚D¿÷'/ýJ

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Python 3, 104 bytes

9 bytes thanks to Felipe Nardi Batista.

from fractions import*
def f(*t):c=[Fraction(*t)for t in zip(*t)];print('+'.join(map(str,c)),'=',sum(c))

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