Mathematics Asked by Ispring Quiz on December 20, 2020
$$frac1{x} = 4$$
If multiplied by $x$ both sides,
$$1 = 4x$$
Then it looks like linear equation in one variable. But is such multiplication by variable on both sides allowed?
The two expressions are equivalent within the condition that $xneq 0$ indeed for $x=0$ we would obtain
which are undefined.
We can observe that as equations in the unknown $x$ they are equivalent in the sense that they lead to the same solution $x=frac14$.
Otherwise for the expressions $frac {x^3}{x}=1$ and $x^3=x$ are not equivalent as equations because $x=0$ is a solution for the second one but not for the first one.
Correct answer by user on December 20, 2020
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