Question 63090

(8x^2- 2x - 3)/(6x^2 - 5x - 4)

Here we factorise the numerator and denominator separately.

8x^2- 2x - 3 = 8x^2 + 4x - 6x - 3

             = 4x(2x + 1) - 3(2x + 1)

             = (2x + 1) (4x - 3)


6x^2 - 5x - 4 = 6x^2 + 3x - 8x - 4

              = 3x(2x + 1) - 4(2x + 1)

              = (2x + 1)(3x - 4)

Thus (8x^2- 2x - 3)/(6x^2 - 5x - 4)
 = (2x + 1) (4x - 3)/  (2x + 1)(3x - 4)

= (4x - 3) / (3x - 4)


Good Luck !!!