Question

PLEASE HELP IT'S URGENT! :(

Find all values of $x$ such that
[\frac{x}{x - 5} = \frac{4}{2x - 4} + 2.\]

Answer 1

Answer:

x/(x - 5) = 4/(2x - 4) + 2

x(2x - 4) = 4(x - 5) + 2(2x - 4)(x - 5)

2x² - 4x = 4x - 20 + 2(2x² - 14x + 20)

2x² - 4x = 4x - 20 + 4x² - 28x + 40

2x² - 4x = 4x² - 24x + 20

2x² - 20x + 20 = 0

x² - 10x + 10 = 0

x² - 10x + 25 = 15

(x - 5)² = 15

x - 5 = ±√15

x = 5 ± √15