How do you find all vertical asymptotes of g(x)=2x+3/((2x^2)+x-3)

Question

anonymous · Answer

Vertical asymptotes will occur where g(x) goes to positive or negative infinity. You should try a few values for x to get a feel for the function, The most common scenario for this to happen is when the denominator of a fraction will go to zero at some value of x. In this case: $2x^2+x-3$ is zero. Solve for x. http://www.wolframalpha.com/input/?i=+g%28x%29%3D2x%2B3%2F%28%282x^2%29%2Bx-3%29

anonymous · Answer

i know that but im confused with how im going to get rod of the 2x^2, what do i do?

anonymous · Answer

Thanks

anonymous · Answer

You should factorise $2x^2+x-3$, to get the values of x where the denominator will be zero. You can factorise by looking, or by using the quadratic formula:
$$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$$, where your quadratic is in the form $ax^2+bx+c$