Help - please solve for x.
$\displaystyle \frac {x + 5}{x} - \frac {8}{2x - 3} = 0$
Thank you
Get a common denominator
$\displaystyle \frac{(2x - 3)(x + 5)}{x(2x - 3)} - \frac{8x}{x(2x - 3)} = 0$
$\displaystyle \frac{(2x - 3)(x + 5) - 8x}{x(2x - 3)} = 0$
First, note that the denominator can not be 0, so $\displaystyle x \neq 0$ and $\displaystyle x \neq \frac{3}{2}$.
$\displaystyle (2x - 3)(x + 5) - 8x = 0$
$\displaystyle 2x^2 + 10x - 3x - 15 - 8x = 0$
$\displaystyle 2x^2 - x - 15 = 0$
$\displaystyle 2x^2 - 6x + 5x - 15 = 0$
$\displaystyle 2x(x - 3) + 5(x - 3) = 0$
$\displaystyle (x - 3)(2x + 5) = 0$
$\displaystyle x = 3$ or $\displaystyle x = -\frac{5}{2}$.