Answer
$(x+7)(x-5)(x+2)$.
Work Step by Step
The given expressions are
$\frac{x+7}{x^2+2x-35}$ and $\frac{x}{x^2+9x+14}$
Factor $x^2+2x-35$.
Rewrite the middle term $2x$ as $7x-5x$
$=x^2+7x-5x-35$
Group terms.
$=(x^2+7x)+(-5x-35)$
Factor each term.
$=x(x+7)-5(x+7)$
Factor out $(x+7)$.
$=(x+7)(x-5)$
Factor $x^2+9x+14$.
Rewrite the middle term $9x$ as $7x+2x$
$=x^2+7x+2x+14$
Group terms.
$=(x^2+7x)+(2x+14)$
Factor each term.
$=x(x+7)+2(x+7)$
Factor out $(x+7)$.
$=(x+7)(x+2)$
LCM $=$ greatest power of all prime factors from both denominators.
LCM $ =(x+7)(x-5)(x+2)$.
