Question 1059713
<font color=black size=3>Let's factor out {{{x^3+7x^2+12x}}} which is the denominator on the left side.


{{{x^3+7x^2+12x}}}


{{{x(x^2+7x+12)}}}


{{{x(x+3)(x+4)}}}


Looking at that factorization and comparing it to x(x+5)(x+3)(x+4), which is the denominator on the right side, all we're missing is (x+5).


So multiply top and bottom of the fraction on the left by (x+5) to get


{{{x/(x^3+7x^2+12x) = x/(x(x+3)(x+4))}}}


{{{x/(x^3+7x^2+12x) = (x*highlight((x+5)))/(x(x+3)(x+4)*highlight((x+5)))}}}


{{{x/(x^3+7x^2+12x) = (x(x+5))/(x(x+5)(x+3)(x+4))}}}


This means that <font color=red>x(x+5)</font> will go where the question mark is. </font>