Question

1. In the rational function: y = (x ^ 2 + 7) / (2x ^ 2 + x - 3) the vertical asymptotes are:

Answer 1

Given the rational function;

$y=\frac{x^2+7}{2x^2+x-3}$

The vertical asymptotes are the points where the denominator is zero;

Thus, we have;

$2x^2+x-3=0$

Then,

$\begin{gathered} 2x^2-2x+3x-3=0 \\ 2x(x-1)+3(x-1)=0 \\ 2x+3=0\text{ or x-1 = 0} \\ x=-\frac{3}{2}\text{ or x = 1} \\ \end{gathered}$

CORRECT OPTION: D