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

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Answer 1 · 2016-05-26T21:18:17

This question has something wrong with it!!!!

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

Move $5/(m-5)$ to the left of the equals and change its sign

$m/(m-5)-5/(m-5)-6=0$

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

$m/(m-5)-5/(m-5)=6$

Multiply moth sides by $(m-5)$

$m-5=6(m-5)$

$color(red)("There is something very wrong with the question")$

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

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