What is the quotient of the rational expression shown below?

Question

asked Oct 10, 2020 118k views

1 Answer

Philonous · Answer 1 · 2020-10-14T21:47:28+0000

First of all, remember that dividing by a fraction is the same as multiplying by the inverse of that fraction:

$(x^2-4)/(x+3)/(x^2-4x+4)/(4x+12)=(x^2-4)/(x+3)\cdot(4x+12)/(x^2-4x+4)$

Now, we can factor all numerators and denominators:

$(x^2-4)/(x+3)\cdot(4x+12)/(x^2-4x+4)=((x+2)(x-2))/(x+3)\cdot(4(x+3))/((x-2)^2)$

and simplify whatever appears at both numerator and denominator:

$((x+2))/(1)\cdot(4)/((x-2))=(4(x+2))/(x-2)$