Question

How do you simplify `(x+5)/(x-3)*(7x^2 - 21x) / (7x)`?

Answer 1

`x+5`

Explanation:

Completely factor out all expressions. You can factor out 7x from `(7x^2-21x)`.

`(x+5)/(x-3)*(7x^2-21x)/(7x)`

`=(x+5)/(x-3)*[(7x)(x-3)]/(7x)`

`=[(x+5)(7x)(x-3)]/[(7x)(x-3)]`

After you have factored everything out, cancel factors that appear in both the numerator and the denominator. In this problem, `7x` and `(x-3)` appear in both the numerator and denominator, so you can cancel them.

`[(x+5)cancel((7x))cancel((x-3))]/[cancel((7x))cancel((x-3))]`

`=(x+5)/1`

`=x+5`