## Algebra 1: Common Core (15th Edition)

Simplified expression: $\frac{2x+3}{2x-1}$ Excluded values: $\frac{1}{2}$ and $4$.
$\frac{2x^2-5x-12}{2s^2-9x+4}$ 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: $\frac{2x^2-5x-12}{2s^2-9x+4}$ $=\frac{2x^2-8x+3x-12}{(2x-1)(x-4)}$ $=\frac{(2x+3)(x-4)}{(2x-1)(x-4)}$ $=\frac{2x+3}{2x-1}$