Answer
x=-8
Work Step by Step
Original Equation
$\frac{x^{2} - 23}{2x^{2} - 5x - 3}$ + $\frac{2}{x-3}$ = $\frac{-1}{2x+1}$
Multiply equation by the LCD, (2x+1)(x-3) to get rid of denominators
$x^{2}$-23 + 2(2x+1) = -(x-3)
Distribute
$x^{2}$+4x-21 = -x+3
Adjust equation to equal 0
$x^{2}$+5x-24=0
Factor
(x+8)(x-3)=0
x=-8, x=3
However, x cannot equal 3 because it would set the denominator equal to 0, so the solution is x=-8
