Step-by-step explanation:
a)
9x² - 4 = (3x + 2)×(3x - 2)
6x - 4 = 2×(3x - 2)
x² - 5x = x(x - 5)
(3x + 2)×(3x - 2) / (2×(3x - 2)) =
(3x + 2) / 2
3x / (x(x - 5) = 3 / (x - 5)
now let's multiply the 2 transformed fractions :
(3x + 2)/2 × 3/(x - 5) = (3×(3x + 2)) / (2×(x - 5)) =
= (9x + 6) / (2x - 10)
b)
4/(x + 2) + 1/(x- 1) - 5/x
(4x(x - 1) + x(x + 2) - 5(x + 2)(x - 1)) / (x(x+2)(x-1))
the numerator (upper part of the fraction) is then
4x² - 4x + x² + 2x - 5(x² - x + 2x - 2) =
= 5x² - 2x - 5(x² + x - 2) = 5x² - 2x - 5x² - 5x + 10 =
= -7x + 10
