Question

How do you perform the indicated operations in `\frac { 5x ^ { 2} - 9x - 2} { y ^ { 2} + 2y - 3} \cdot \frac { y ^ { 2} + 4y - 5} { 20x ^ { 2} + 9x + 1} \div \frac { 7x ^ { 2} - 12x - 4} { 8x ^ { 2} - 10x - 3}`?

Answer 1

`((y+5)(2x-3))/((y+3)(7x+2))`

Explanation:

Given: `(5x^2 - 9x - 2)/(y^2 +2y-3) * (y^2 + 4y - 5) / (20x^2 + 9x + 1) -: (7x^2 - 12x - 4)/(8x^2 - 10x - 3)`

First change the last term to a multiplication by reciprocating the term `("Ex. " 2/3 -: 4/7 = 2/3 * 7/4)`:

`(5x^2 - 9x - 2)/(y^2 +2y-3) * (y^2 + 4y - 5)/(20x^2 + 9x + 1) * (8x^2 - 10x - 3)/(7x^2 - 12x - 4)`

Factor each polynomial:

`((5x+1)(x-2))/((y-1)(y+3)) * ((y+5)(y-1))/((4x+1)(5x+1)) * ((4x+1)(2x-3))/((7x+2)(x-2))`

Cancel factors that are both in the numerator and denominator:

`(cancel(5x+1)cancel((x-2)))/(cancel(y-1)(y+3)) * ((y+5)cancel(y-1))/(cancel((4x+1))cancel(5x+1)) * (cancel((4x+1))(2x-3))/((7x+2)cancel((x-2)))`

Simplify:`((y+5)(2x-3))/((y+3)(7x+2))`