# How do you solve (r-4)/(5r)=1/(5r)+1 and check for extraneous solutions?

Jul 9, 2017

Solution : $r = - \frac{5}{4}$

#### Explanation:

$\frac{r - 4}{5 r} = \frac{1}{5 r} + 1$. multiplying by $5 r$ on both sides , we get,

$r - 4 = 1 + 5 r \mathmr{and} 5 r - r = - 4 - 1 \mathmr{and} 4 r = - 5 \mathmr{and} r = - \frac{5}{4}$

Solution : $r = - \frac{5}{4}$

Check: L.H.S $= \frac{r - 4}{5 r} = \frac{- \frac{5}{4} - 4}{5 \cdot \left(- \frac{5}{4}\right)} = \frac{- \frac{21}{\cancel{4}}}{- \frac{25}{\cancel{4}}} = \frac{21}{25}$

R.H.S $= \frac{1}{5 r} + 1 = \frac{1}{5 \cdot \left(- \frac{5}{4}\right)} + 1 = - \frac{4}{25} + 1 = \frac{21}{25}$

$\therefore R . H . S = L . H . S$ {checked) [Ans]