[tex]\frac{y^{2} + 3y - 4}{2y^{2} - 32} = \frac{y^{2} + 4y - y - 4}{2(y^{2}) - 2(16)} = \frac{y(y) + y(4) - 1(y) - 1(4)}{2(y^{2} - 16)} = \frac{y(y + 4) - 1(y - 4)}{2(y(y + 4) - 4(y + 4))} = \frac{(y + 1)(y - 4)}{2(y - 4)(y + 4)} = \frac{y + 1}{2(y + 4)} = \frac{y + 1}{2y + 8}[/tex]
