Question

Simplify the following rational expression. 5a - 10 6a - 12 5a - 10 62 -12 (Simplify your answer. Type an integer or a fraction.)

Please answer both questions

Answer 1

(5a - 10)/(6a - 12)

= (5(a - 2))/(6(a - 2))

= (5/6)*((a-2)/(a-2))

= (5/6)*1

= 5/6

implies (5a - 10)/(6a - 12) = 5/6

(2x² - 5x -12)/(x² - 5x + 4)

First let us factorize both numerator and denominator

Factorizing 2x² - 5x - 12 we get

2x² - 5x - 12

= 2x² - 8x + 3x - 12

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

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

implies 2x² - 5x - 12 = (x - 4)(2x + 3)

Factorizing x² - 5x + 4 we get

x² - 5x + 4

= x² - x - 4x + 4

= x(x - 1) - 4(x - 1)

= (x - 1)(x - 4)

implies x² - 5x + 4 = (x - 1)(x - 4)

Now

(2x² - 5x - 12)/(x² - 5x + 4)

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

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

implies (2x² - 5x - 12)/(x² - 5x + 4) = (2x + 3)/(x - 1)