# How do you simplify (3x)/4-(5x)/6?

Mar 30, 2017

$\frac{3 x}{4} - \frac{5 x}{6} = - \frac{x}{12}$

#### Explanation:

$\frac{3 x}{4} - \frac{5 x}{6}$

$\textcolor{red}{\frac{3}{3}} \cdot \frac{3 x}{4} - \textcolor{b l u e}{\cdot \frac{2}{2}} \frac{5 x}{6}$

$\frac{9 x}{12} - \frac{10 x}{12}$

$\frac{9 x - 10 x}{12}$

$- \frac{x}{12}$

Mar 30, 2017

$- \frac{x}{12}$

#### Explanation:

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

Multiplying the numerator/denominator of $\frac{3 x}{4}$ by 6 and

$\frac{5 x}{6}$ by 4 will ensure this.

$\left(\frac{3 x}{4} \times \frac{6}{6}\right) - \left(\frac{5 x}{6} \times \frac{4}{4}\right)$

$= \frac{18 x}{24} - \frac{20 x}{24}$

Now there is a common denominator we can subtract the numerators leaving the denominator as it is.

$= \frac{- 2 x}{24} = - \frac{{\cancel{2}}^{1} x}{\cancel{24}} ^ 12 = - \frac{x}{12}$