# How do you solve \frac { 3} { m - 4} = \frac { m } { m - 2}?

May 20, 2018

$m = 6 \mathmr{and} m = 1$

#### Explanation:

If you have an equation which has fractions, you can get rid of the denominators immediately by multiplying each side of the equation by the LCM of the denominators.

In this case it is $\textcolor{b l u e}{\left(m - 4\right) \left(m - 2\right)}$

$\frac{3 \times \textcolor{b l u e}{\cancel{\left(m - 4\right)} \left(m - 2\right)}}{\cancel{\left(m - 4\right)}} = \frac{m \times \textcolor{b l u e}{\left(m - 4\right) \left(\cancel{m - 2}\right)}}{\cancel{\left(m - 2\right)}}$

We are left with:

$3 \left(m - 2\right) = m \left(m - 4\right) \text{ } \leftarrow$ multiply into the brackets

$3 m - 6 = {m}^{2} - 4 m \text{ } \leftarrow$ a quadratic. Make it $= 0$

$0 = {m}^{2} - 4 m - 3 m + 6$

${m}^{2} - 7 m + 6 = 0 \text{ } \leftarrow$ factorise

$\left(m - 6\right) \left(m - 1\right) = 0$

Solve each factor set equal to $0$

$m = 6 \mathmr{and} m = 1$

Neither of these will make the denominators $0$, so both are possible answers.