This equation keep giving me error messages

Question

I am trying to post a  explanation on aops and it keeps saying

Error compiling LaTeX. ! File ended while scanning use of align*.

Please get back ASAP, it's homework thanks in advance.
begin{align*}
frac{6sqrt{{(x+1)(x+3)+1}-12}{2x}
&=frac{6sqrt{x^2+4x+3+1}-12}{2x}
&=frac{6sqrt{x^2+4x+4}-12}{2x}
&=frac{6(x+2)-12}{2x}
&=frac{6x+12-12}{2x}
&=frac{6x}{2x}=3
end{align*}

muzimuzhi Z · Accepted Answer

Note

align* environment enters math mode for you, so there is node need to wrap it in between $$ ... $$.
The left brace of numerator of first frac is never closed by a pairing right brace.
You might need & mathrel{phantom{=}} prepended to first line of align*.

documentclass{article}
usepackage{amsmath}

begin{document}
begin{align*}
     & mathrel{phantom{=}}frac{6sqrt{{(x+1)(x+3)+1}-12}}{2x} 
     & =frac{6sqrt{x^2+4x+3+1}-12}{2x}                         
     & =frac{6sqrt{x^2+4x+4}-12}{2x}                           
     & =frac{6(x+2)-12}{2x}                                     
     & =frac{6x+12-12}{2x}                                      
     & =frac{6x}{2x}=3
end{align*}
end{document}

Leucippus · Answer

Errors in the first line are the cause, ie mismatched { }. A fix is:
begin{align*}
frac{6sqrt{(x+1)(x+3)+1}-12}{2x}
&=frac{6sqrt{x^2+4x+3+1}-12}{2x} 
&=frac{6sqrt{x^2+4x+4}-12}{2x} 
&=frac{6(x+2)-12}{2x} 
&=frac{6x+12-12}{2x} 
&=frac{6x}{2x} = 3
end{align*}

which produces:

Zarko · Answer

Your problems is already solved in other answers, but you may liked the following solution which employ the instruction MoveEqLeft defined in the mathtools package:
documentclass{article}
usepackage{mathtools}

begin{document}
begin{align*}
    MoveEqLeft[3]
frac{6sqrt{{(x+1)(x+3)+1}-12}}{2x}        
     & =frac{6sqrt{x^2+4x+3+1}-12}{2x}     
       =frac{6sqrt{x^2+4x+4}-12}{2x}       & =frac{6(x+2)-12}{2x}                 
       =frac{6x+12-12}{2x}                 
     & =frac{6x}{2x}=3
end{align*}
end{document}

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This equation keep giving me error messages

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