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?

Algebra ->  Polynomials-and-rational-expressions -> 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?      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
%2812%29%2F%28x%29-%2812%29%2F%28x-1%29=-1 Start with the given equation.


Multiply EVERY term on both sides by the LCD x%28x-1%29. Doing this will eliminate all of the fractions.


12%28x-1%29-12x=-x%28x-1%29 Multiply and simplify (I also rearranged some terms)


12x-12-12x=-x%5E2%2Bx Distribute


-12=-x%5E2%2Bx Combine like terms.


0=-x%5E2%2Bx%2B12 Add 12 to both sides.


%28-x%2B4%29%28x%2B3%29=0 Factor the left side (note: if you need help with factoring, check out this solver)



Now set each factor equal to zero:
-x%2B4=0 or x%2B3=0

x=4 or x=-3 Now solve for x in each case


So our answers are

x=4 or x=-3