Question

How do you solve this?

Answer 1

9(x + 3)

Explanation:

`(2x^2 + x - 15)/(2x^2 - 11x - 21) * (6x + 9) / (2x - 5)/(3x - 21) =`

Change division into multiplication by reciprocal.

`= (2x^2 + x - 15)/(2x^2 - 11x - 21) * (6x + 9) * (3x - 21)/(2x - 5)`

Factor every polynomial.

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

Combine all factors into a single fraction.

`= (9(2x - 5)(x + 3)(2x + 3)(x - 7))/((x - 7)(2x + 3)(2x - 5))`

Rearrange terms and separate fractions to see what simplifies.

`= (9(x + 3))/(1) * (2x - 5)/(2x - 5) * (2x + 3)/(2x + 3) * (x - 7)/(x - 7)`

Cancel each pair of equal factors in the numerator and denominator.

`= (9(x + 3))/(1)`

Simplify.

`= 9(x + 3)`