Question

divide.
\\(\dfrac{49x^2 - 25}{2x^2 + x - 21} \div \dfrac{7x + 5}{4x - 12}\\)
simplify your answer as much as

Explanation:

Step1: Rewrite division as multiplication

$\frac{49x^2 - 25}{2x^2 + x - 21} \times \frac{4x - 12}{7x + 5}$

Step2: Factor all expressions

$49x^2 -25=(7x-5)(7x+5)$; $2x^2+x-21=(2x+7)(x-3)$; $4x-12=4(x-3)$
Substitute factored forms:
$\frac{(7x-5)(7x+5)}{(2x+7)(x-3)} \times \frac{4(x-3)}{7x+5}$

Step3: Cancel common factors

Cancel $(7x+5)$ and $(x-3)$:
$\frac{(7x-5) \times 4}{2x+7}$

Step4: Simplify the expression

$\frac{4(7x-5)}{2x+7} = \frac{28x - 20}{2x + 7}$

Answer:

$\frac{28x - 20}{2x + 7}$ (or $\frac{4(7x-5)}{2x+7}$)