Question

How do you solve `2/x + 1/(x+1) = 5/(x^2+x)`?

Answer 1

You may have noticed, that `x^2+x=x*(x+1)`

So we may multiply every part of the equation by `x*(x+1)` and get rid of all the denominators.
BUT: `x!=0andx!=-1` or one of the denominators `=0`

The equation goes into:
`->2*(x+1)+x=5->3x=3->` `x=1`
And this is allowed.

Always check the answer:

`2/1+1/(1+1)=5/(1^2+1)=2 1/2`