Question

What is the quotient of the rational expression shown below?

Answer 1

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)`