SOLUTION: Hello I was just hoping that someone could help clarify an answer for me. 10/(x^2+x-6)+ 3x/(x^2-4x+4) This has already been solved on the website but my problem is that I do

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Hello I was just hoping that someone could help clarify an answer for me. 10/(x^2+x-6)+ 3x/(x^2-4x+4) This has already been solved on the website but my problem is that I do      Log On


   



Question 869040: Hello I was just hoping that someone could help clarify an answer for me.
10/(x^2+x-6)+ 3x/(x^2-4x+4)
This has already been solved on the website but my problem is that I do not understand why the steps were carried out as they were. Could someone solve this for me again with a more detailed explanation? For instance I cant figure out why this [10(x-2) + 3x (x+3)]/ [(x+3)(x-2)^2] is going on. Why am I multiplying 10(x-2) and 3x(x+3)? I think that the operation for dealing with the perfect square trinomial (x-2)^2 is what's throwing me off. Please help! Thank you!

Found 2 solutions by josgarithmetic, Theo:
Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
The addition of the two rational expressions requires changing each rational expression into an equivalent one using the simplest common denominator (like Lowest Common Denominator.)

x%5E2%2Bx-6=%28x-2%29%28x%2B3%29 and x%5E2-4x%2B4=%28x-2%29%28x-2%29.
These as denominators mean that the "lowest" common denominator is %28x-2%29%28x-2%29%28x%2B3%29.

The first summand,
;

and you will use a different factor of 1 for the second summand.

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
your problem is:

10%2F%28x%5E2%2Bx-6%29%2B+3x%2F%28x%5E2-4x%2B4%29

x^2 + x - 6 factors out to be (x+3) * (x-2)

x^2 - 4x + 4 factors out to be (x-2) * (x-2)

your expression becomes:

10+%2F+%28%28x%2B3%29%28x-2%29%29+%2B+3x+%2F+%28%28x-2%29%28x-2%29%29

in order to add these together, they have to have the same denominator.

you have to multiply the first fraction on the left by %28x-2%29+%2F+%28x-2%29.

you have to multiply the second fraction on the right by %28x%2B3%29+%2F+%28x%2B3%29.

you will get:

%2810%2A%28x-2%29%2B3x%2A%28x%2B3%29%29%2F%28%28x%2B3%29%2A%28x-2%29%2A%28x-2%29%29

since the denominators are now the same, you can add the numerators together under the common denominator to get:

i believe that's your solution.

i took it one step further to get:

%283x%5E2%2B19x-20%29%2F%28%28x%2B3%29%2A%28x-2%29%5E2%29%29%29