Respuesta :
Answer:
see explanation
Step-by-step explanation:
Given
[tex]\frac{x^2-4}{x+3}[/tex] ÷ [tex]\frac{x^2-4x+4}{4x+2}[/tex]
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
[tex]\frac{(x-2)(x+2)}{x+3}[/tex] × [tex]\frac{2(2x+1)}{(x-2)(x-2)}[/tex]
Final step is to cancel common factors from the numerators/denominators
= [tex]\frac{2(2x+1)(x+2)}{(x+3)(x-2)}[/tex] ← quotient
