# How do you find (f/g)(2) given f(x)=x^2-1 and g(x)=2x-3 and h(x)=1-4x?

Aug 16, 2017

See a solution process below:

#### Explanation:

First, we can write $\left(\frac{f}{g}\right) \left(x\right)$ as:

$\left(\frac{f}{g}\right) \left(x\right) = \frac{{x}^{2} - 1}{2 x - 3}$

We can now substitute $\textcolor{red}{2}$ for each occurrence of color(red)(x)$\in$(f/g)(x) and calculate the result:

$\left(\frac{f}{g}\right) \left(\textcolor{red}{x}\right) = \frac{{\textcolor{red}{x}}^{2} - 1}{2 \textcolor{red}{x} - 3}$ becomes:

$\left(\frac{f}{g}\right) \left(\textcolor{red}{2}\right) = \frac{{\textcolor{red}{2}}^{2} - 1}{\left(2 \cdot \textcolor{red}{2}\right) - 3}$

$\left(\frac{f}{g}\right) \left(\textcolor{red}{2}\right) = \frac{4 - 1}{4 - 3}$

$\left(\frac{f}{g}\right) \left(\textcolor{red}{2}\right) = \frac{3}{1}$

$\left(\frac{f}{g}\right) \left(\textcolor{red}{2}\right) = 3$

The $h \left(x\right)$ function is extraneous information in this problem.