Answer:
x-5/x+3 = (x² - 2x -15)/(x² - 9)
4/x-3 = (4x + 12)/(x² - 9)
Step-by-step explanation:
Points to remember
(a + b)(a - b) = a² - b²
It is given two expression,
x-5/x+3 and 4/x-3
To find the common denominator
The first denominator is (x + 3) and the second denominator is (x - 3)
The common denominator is (x + 3)(x -3)
x-5/x+3 can be written as,
(x-5)/(x+3) * (x - 3)/(x - 3)
= (x² -5x + 3x -15)/(x² - 9)
= (x² - 2x -15)/(x² - 9)
4/(x - 3) can be written as,
4/(x - 3) * (x + 3)(x + 3)
= 4(x + 3)/(x - 3)(x + 3)
= (4x + 12)/(x² - 9)
Therefore x-5/x+3 and 4/x-3 in common denominator is,
x-5/x+3 = (x² - 2x -15)/(x² - 9)
4/x-3 = (4x + 12)/(x² - 9)
