Let f(x) = 6x^2 + 7x - 5 and g(x) = 2x - 1, how do you find f/g?

May 26, 2017

See a solution process below:

Explanation:

$\left(\frac{f}{g}\right) \left(x\right) = \frac{6 {x}^{2} + 7 x - 6}{2 x - 1}$

We can then factor the numerator:

$\left(\frac{f}{g}\right) \left(x\right) = \frac{\left(2 x - 1\right) \left(3 x + 5\right)}{2 x - 1}$

We can now cancel common terms in the numerator and denominator:

$\left(\frac{f}{g}\right) \left(x\right) = \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{\left(2 x - 1\right)}}} \left(3 x + 5\right)}{\textcolor{red}{\cancel{\textcolor{b l a c k}{2 x - 1}}}}$

$\left(\frac{f}{g}\right) \left(x\right) = 3 x + 5$

Where:

$\left(2 x - 1\right) \ne 0$

Or

$x \ne \frac{1}{2}$