How do you solve #1/(m^2-m)+1/m=5/(m^2-m)# and check for extraneous solutions?
on both sides we get,
On check ,
In a problem like this we can assume the denominators are not zero, so we never really run into extraneous solutions
Sometimes extraneous solutions are unavoidable, as often happens when we have to square both sides of an equation.
That's not the case in a problem like this. We can at the outset assume the denominators are not zero, i.e assume
Usually we must always factor, never cancel. But when we know factors are non-zero, we can cancel them.