Question

Solve the rational equation:. x+3/3x-2 minus x-3/3x+2=44/9x^2-4

Answer 1

$\frac{x+3}{3x-2} - \frac{x-3}{3x+2} = \frac{44}{9x^2-4}$
$\frac{(x+3)(3x+2) - (x-3)(3x-2)}{(3x-2)(3x+2)} = \frac{44}{(3x+2)(3x-2)}$

$(x+3)(3x+2) - (x-3)(3x-2) = 44$
$(3x^2 + 11x + 6) - (3x^2 - 11x + 6) = 44$
$22x = 44$
$x = 2$Substituting x = 2 into the original does not give any extraneous solutions, so this is the answer.