SOLUTION: I dont understand this problem any help is appreciated, Thank you! x/x-4- 1/x-1 divided by x/x-1+ 2/x-3

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I dont understand this problem any help is appreciated, Thank you! x/x-4- 1/x-1 divided by x/x-1+ 2/x-3      Log On


   

Question 57355: I dont understand this problem any help is appreciated, Thank you!
x/x-4- 1/x-1 divided by x/x-1+ 2/x-3
Found 2 solutions by stanbon, funmath:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
[x/(x-4)- 1/(x-1)] / [x/(x-1)+ 2/(x-3)]
-------------------
Numerator : [x(x-1)-(x-4)]/[(x-4)(x-1)]
=[x^2-x-x+4]/[[x^2-5x+4]
=[x^2-2x+4]/[x^2-5x+4]
----------
Denominator: [x(x-3+2(x-1)]/[x^2-4x+3]
=[x^2-3x+2x-2]/[x^2-4x+3]
=[x^2-x-2]/[x^2-4x+3]
-------------
Invert the denominator and multiply to get:
[x^2-2x+4/[(x-4)(x-1)] * [(x-3)(x-1)]/[(x-2)(x+1)]
Cancel the (x-1)'s to get:
[(x^2-2x+4)(x-3)]/[(x-4)(x-2)(x+1)]
Cheers,
Stan H.

Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
If this is what you meant:
x%2F%28x-4%29-1%2F%28x-1%29 divided by x%2F%28x-1%29%2B2%2F%28x-3%29
This is how you do it: It's probably easiest to turn this into two fractions then divide rather than using the methods commonly used for complex fractions.
x%2F%28x-4%29-1%2F%28x-1%29 divided by x%2F%28x-1%29%2B2%2F%28x-3%29
:
The LCD for the 1st fraction is: (x-4)(x-1) whatever you do to the denominator to get that, you also do to the numerator:
x%28x-1%29%2F%28%28x-4%29%28x-1%29%29-1%28x-4%29%2F%28%28x-4%29%28x-1%29%29
%28x%5E2-x%29%2F%28%28x-4%29%28x-1%29%29%2B%28-x%2B4%29%2F%28%28x-4%29%28x-1%29%29
%28x%5E2-x-x%2B4%29%2F%28%28x-4%29%28x-1%29%29
%28x%5E2-2x%2B4%29%2F%28%28x-4%29%28x-1%29%29
:
The LCD for the 2nd fraction is: (x-1)(x-3)
x%28x-3%29%2F%28%28x-1%29%28x-3%29%29%2B2%28x-1%29%2F%28%28x-1%29%28x-3%29%29
%28x%28x-3%29%2B2%28x-1%29%29%2F%28%28x-1%29%28x-3%29%29
%28x%5E2-3x%2B2x-2%29%2F%28%28x-1%29%28x-3%29%29
%28x%5E2-x-2%29%2F%28%28x-1%29%28x-3%29%29
:
Now you have:
%28x%5E2-2x%2B4%29%2F%28%28x-4%29%28x-1%29%29 divided by %28x%5E2-x-2%29%2F%28%28x-1%29%28x-3%29%29 Flip the second fraction and multiply:


%28%28x%5E2-2x%2B4%29%2F%28x-4%29%29%2A%28%28x-3%29%2F%28x%5E2-x-2%29%29
%28x-3%29%28x%5E2-2x%2B4%29%2F%28%28x-4%29%28x%5E2-x-2%29%29
Happy Calculating, that was a whopper!!!