Solve for x: 4 over x plus 4 over quantity x squared minus 9 equals 3 over quantity x minus 3

x = - 4 and x = - 9

x = 4 and x = - 9

x = - 4 and x = 9

x = 4 and x = 9

Step-by-step explanation:

4/x + 4 / (x²-9) = 3 / (x - 3)

4 / x + 4 / [ (x - 3) (x + 3) ] = 3 / (x - 3) / * x (x - 3) (x + 3)

Restrictions : x ≠ 0, x ≠ - 3, x ≠ 3;

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

4 (x² - 9) + 4 x = 3 x² + 9 x

4 x² - 36 + 4 x - 3 x² - 9 x = 0

x² - 5 x - 36 = 0

x² - 9 x + 4 x - 36 = 0

x (x - 9) + 4 (x - 9) = 0

(x - 9) (x + 4) = 0

x - 9 = 0, or : x + 4 = 0

Answer:

x = 9, x = - 4