Question

What is the quotient of the rational expression shown below? Make sure your answer is in reduced form x^2-4/x+3 divided x^2-4x+4/4x+2

Answer 1

Answer:

see explanation

Step-by-step explanation:

Given

$\frac{x^2-4}{x+3}$ ÷ $\frac{x^2-4x+4}{4x+2}$

The first step is to factor numerators/denominators, if possible

x² - 4 = (x - 2)(x + 2) ← difference of squares

x² - 4x + 4 = (x - 2)(x - 2) ← perfect square

4x + 2 = 2(2x + 1)

To divide the expressions follow the steps

• Leave the first fraction

• Change division to multiplication

• Turn the second fraction upside down

We now have

$\frac{(x-2)(x+2)}{x+3}$ × $\frac{2(2x+1)}{(x-2)(x-2)}$

Final step is to cancel common factors from the numerators/denominators

= $\frac{2(2x+1)(x+2)}{(x+3)(x-2)}$ ← quotient