Question

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

Answer 1

`(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)`