How do you simplify \frac { ( 3x ^ { 2} + 15x ) } { x ^ { 2} - 3x - 40} \div \frac { 5x ^ { 2} } { x ^ { 2} - 64}(3x2+15x)x23x40÷5x2x264?

1 Answer
Nov 9, 2017

(3(x+8))/(5x)3(x+8)5x

Explanation:

The expression can be rewritten as:
(3x^2+15x)/(x^2-3x-40)*(x^2-64)/(5x^2)3x2+15xx23x40x2645x2

We can factor out some terms.
((3x)(x+5))/((x-8)(x+5))*((x-8)(x+8))/(5x^2)(3x)(x+5)(x8)(x+5)(x8)(x+8)5x2

Simplifying:
((3cancelx)cancel((x+5)))/(cancel((x-8))cancel((x+5)))*(cancel((x-8))(x+8))/(5x^cancel2)

(3(x+8))/(5x)