# How do you solve 10/(x + 4) = 15/(4x + 4) and find any extraneous solutions?

Nov 20, 2017

Solution: $x = \frac{4}{5}$

#### Explanation:

$\frac{10}{x + 4} = \frac{15}{4 x + 4}$ Multiplying by $\left(x + 4\right) \left(4 x + 4\right)$ on

both sides we get $10 \left(4 x + 4\right) = 15 \left(x + 4\right)$ or

$40 x + 40 = 15 x + 60 \therefore 25 x = 20 \mathmr{and} x = \frac{20}{25} = \frac{4}{5}$

Check: L.H.S $= \frac{10}{x + 4} = \frac{10}{\frac{4}{5} + 4} = \frac{10}{\frac{24}{5}} = \frac{50}{24} = \frac{25}{12}$

R.H.S $= \frac{15}{4 x + 4} = \frac{15}{4 \cdot \frac{4}{5} + 4} = \frac{15}{\frac{16}{5} + 4} = \frac{15}{\frac{36}{5}} = \frac{75}{36}$

$\frac{25}{12} \therefore$ L.H.S $=$ R.H.S . No invalid solution to original

problem so there is no extraneous solution.

Solution: $x = \frac{4}{5}$ [Ans]