SOLUTION: x^2-20/x^2-7x+12=3/x-3+5/x-4 Solve Not sure if I am multiplying correct LCD--- (x-4)(x-3) I ended up with (x-7)(x-1) =0! Not sure at all about my answer! Help me! PLEA

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: x^2-20/x^2-7x+12=3/x-3+5/x-4 Solve Not sure if I am multiplying correct LCD--- (x-4)(x-3) I ended up with (x-7)(x-1) =0! Not sure at all about my answer! Help me! PLEA      Log On


   

Question 426028: x^2-20/x^2-7x+12=3/x-3+5/x-4 Solve
Not sure if I am multiplying correct LCD--- (x-4)(x-3)
I ended up with (x-7)(x-1) =0! Not sure at all about my answer! Help me! PLEASE!!!
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
Everything you've done so far is exactly correct! But you are not finished. With the equation
(x-7)(x-1) = 0
the next step is to use the Zero Product Property which tells us that a rpdict can be zero only if one of the factors is zero. So
x-7 = 0 or x-1 = 0
Solving these we get:
x = 7 or x = 1

Last of all we need tocheck our answers. When you multiplied by the LCD, (x-3)(x-4), you multiplied by an expression that cuold be zero (depending on what value x has). Whenever you multiply both sides of an equation by an expresison that could be zero, you must chaek your answers.

Use the original equation to check:
%28x%5E2-20%29%2F%28x%5E2-7x%2B12%29=+3%2F%28x-3%29%2B5%2F%28x-4%29
Checking x = 7:

Simplifying...
%2849-20%29%2F%2849-49%2B12%29+=+3%2F4%2B5%2F3
29%2F12+=+3%2F4%2B5%2F3
At this point we can see that the denominators are not going to be zero. This is the required part of the check. The rest of the check is optional and you are welcome to finish it.

Checking x = 1:

Simplifying...
%281-20%29%2F%281-7%2B12%29+=+3%2F%28-2%29%2B5%2F%28-3%29
%28-19%29%2F6+=+-3%2F2%2B+%28-5%2F3%29
At this point we can see that the denominators are not going to be zero. This is the required part of the check. The rest of the check is optional and you are welcome to finish it.
So there are two solutions to your equation:
x = 7 or x = 1