Question

1. divide: \\(dfrac{x^2 - 49}{x^2 - 14x + 49} div dfrac{5x + 35}{x^2 + 7x}\\)

options:
\\(dfrac{x}{5}\\)
\\(dfrac{5(x - 7)}{x(x + 7)}\\)
\\(dfrac{x + 7}{x - 7}\\)
\\(dfrac{x(x + 7)}{5(x - 7)}\\)

Explanation:

Step1: Factor all expressions

$x^2-49=(x+7)(x-7)$, $x^2-14x+49=(x-7)^2$, $5x+35=5(x+7)$, $x^2+7x=x(x+7)$

Step2: Rewrite division as multiplication

$\frac{(x+7)(x-7)}{(x-7)^2} \times \frac{x(x+7)}{5(x+7)}$

Step3: Cancel common factors

Cancel $(x+7)$ and $(x-7)$: $\frac{x(x+7)}{5(x-7)}$

Answer:

$\frac{x(x+7)}{5(x-7)}$