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

1 Answer
Nov 9, 2017

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

Explanation:

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

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

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

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