# How do you simplify (6g)/(g+5)-(g-2)/(2g)?

Mar 12, 2017

$\frac{11 {g}^{2} - 3 g + 10}{2 g \left(g + 5\right)}$

#### Explanation:

Before we can subtract the fractions we require them to have a
$\textcolor{b l u e}{\text{common denominator}}$

This is achieved by multiplying the numerator/denominator of

$\frac{6 g}{g + 5} \text{ by 2g and the numerator/denominator of } \frac{g - 2}{2 g}$

by (g + 5)

$\Rightarrow \left(\frac{6 g}{g + 5} \times \frac{2 g}{2 g}\right) - \left(\frac{g - 2}{2 g} \times \frac{g + 5}{g + 5}\right)$

$= \frac{12 {g}^{2}}{2 g \left(g + 5\right)} - \frac{\left(g - 2\right) \left(g + 5\right)}{2 g \left(g + 5\right)}$

Now that the fractions have a common denominator we can subtract the numerators, leaving the denominator as it is.

$= \frac{12 {g}^{2} - \left({g}^{2} + 3 g - 10\right)}{2 g \left(g + 5\right)}$

$= \frac{12 {g}^{2} - {g}^{2} - 3 g + 10}{2 g \left(g + 5\right)}$

$= \frac{11 {g}^{2} - 3 g + 10}{2 g \left(g + 5\right)}$