Question

What is the solution to the rational equation (x/x^2-9)-1/x+3=1/4x-12

Answer 1

$( \frac{x}{x {}^{2} - 9 } ) - \frac{1}{x + 3} = \frac{1}{4x - 12}$
$\frac{x}{(x - 3)(x + 3)} - \frac{1}{x + 3} = \frac{1}{4(x - 3)}$
$\frac{x - (x - 3) }{(x - 3)(x + 3)} = \frac{1}{4(x - 3)}$
$\frac{12(x - 3)}{(x - 3)(x + 3)} = 1$
$\frac{12}{x + 3} = 1$
$12 = x + 3 \\ x = 9$