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

x = 9,  x = - 4

more detail

step-by-step explanation: