Answer
$\displaystyle \frac{x+7}{x}$
Work Step by Step
Step by step multiplication of rational expressions:
1. Factor completely what you can
2. Reduce (divide) numerators and denominators by common factors.
3. Multiply the remaining factors in the numerators and
multiply the remaining factors in the denominators. $(\displaystyle \frac{P}{Q}\cdot\frac{R}{S}=\frac{PR}{QS})$
---
Factor what we can:
$x^{2}-49=x^{2}-7^{2}=\qquad $... a difference of squares,
$=(x+7)(x-7)$
$x^{2}-4x-21=...$
... factor the trinomial $x^{2}+bx+c$
... by searching for two factors of $c$ whose sum is $b$.
... Here, we find that $-7$ and $+3 $are factors of $-21$ whose sum is $-4.$
$=(x-7)(x+3)$
The problem becomes
$...=\displaystyle \frac{(x+7)(x-7)\cdot(x+3)}{(x-7)(x+3)\cdot x}\qquad $... divide out the common factors
= $\displaystyle \frac{x+7}{x}$
