66.5k views
3 votes
How do you solve this?

How do you solve this?-example-1
User Ttyyll
by
8.0k points

1 Answer

3 votes

Answer:

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)

User Ricardo Green
by
7.3k points