Answer
Simplified expression: $\frac{2x+3}{2x-1}$
Excluded values: $\frac{1}{2}$ and $4$.
Work Step by Step
$\frac{2x^2-5x-12}{2s^2-9x+4}$
In a rational expression, excluded values are real numbers that make the denominator equal to zero. Therefore, all solutions of the equation $2x^2-9x+4=0$ are excluded values.
$2x^2-9x+4=0$
$2x^2-8x-x+4=0$
$2x(x-4)=(x-4)=0$
$(2x-1)(x-4)=0$
$2x-1=0$ or $x-4=0$
$x=\frac{1}{2}$ or $x=4$
Now, we can simplify the expression:
$\frac{2x^2-5x-12}{2s^2-9x+4}$
$=\frac{2x^2-8x+3x-12}{(2x-1)(x-4)}$
$=\frac{(2x+3)(x-4)}{(2x-1)(x-4)}$
$=\frac{2x+3}{2x-1}$
