# How do you solve (m/(m-5))-6 = 5/(m-5) and find any extraneous solutions?

May 26, 2016

This question has something wrong with it!!!!

#### Explanation:

Mathematically you are not allowed to divide by 0. The proper name for this is: the equation is undefined for $m = 5$

Move $\frac{5}{m - 5}$ to the left of the equals and change its sign

$\frac{m}{m - 5} - \frac{5}{m - 5} - 6 = 0$

Move the 6 to the other side of the equals and change its sign

$\frac{m}{m - 5} - \frac{5}{m - 5} = 6$

Multiply moth sides by $\left(m - 5\right)$

$m - 5 = 6 \left(m - 5\right)$

$\textcolor{red}{\text{There is something very wrong with the question}}$

color(red)(m-5=6(m-5)" end up stating that " 1=6" " ???????)