Question

solve for x: (4 over x) + (4 over x^2-9) = (3 over x-3)

Answer 1

I made a mistake simplifying

(4/x) + (4/(x^(2)-9)) = 3/(x-3)
=
(4(x^(2)-9) + 4x)/x(x^(2)-9) = 3/(x-3)
=
(4x^(2) - 36 + 4x)/x(x^(2)-9) = 3/(x-3)
=
(4x^(2) - 36 + 4x)/x(x-3)(x+3) = 3/(x-3)
=
(4x^(2) - 36 + 4x)(x-3)/x(x-3)(x+3) = 3
=
(4x^(2) + 4x - 36)/x(x+3) = 3

Answer 2

(4x^(2) + 4x - 36)/x(x+3) = 3
=
4(x^(2) + x - 9)/x(x+3) = 3

Answer 3

4(x^(2) + x - 9) = 3x(x+3)
=
4(x^(2) + x - 9) - 3x(x+3) = 0

Answer 4

4(x^(2) + x - 9) - 3x(x+3) = 0
=
4x^(2) + 4x - 36 - 3x^(2) - 9x = 0
=
x^(2) + 5x - 36 = 0
=
(x-9)(x+4) = 0
therefore
9, -4 are your answers