SOLUTION: I am having trouble with 12/x-12/x-1=-1 does not equal 0. I multiply both sides by x-1 and get -12/1+12=x+1, which is also -12+12=x+1, which is 0=x+1. Is x=-1?

Question 167707: I am having trouble with 12/x-12/x-1=-1 does not equal 0. I multiply both sides by x-1 and get -12/1+12=x+1, which is also -12+12=x+1, which is 0=x+1. Is x=-1?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given equation.

Multiply EVERY term on both sides by the LCD . Doing this will eliminate all of the fractions.

Multiply and simplify (I also rearranged some terms)

Distribute

Combine like terms.

Add 12 to both sides.

Factor the left side (note: if you need help with factoring, check out this solver)

Now set each factor equal to zero:
or

or Now solve for x in each case

So our answers are

or