SOLUTION: subtracting rational expressions having different denominators I have a solution to this problem but I need to know if it is correct. 7x^2+15x- 11(numerator )over2x^2-5x+2

Algebra ->  Algebra  -> Polynomials-and-rational-expressions -> SOLUTION: subtracting rational expressions having different denominators I have a solution to this problem but I need to know if it is correct. 7x^2+15x- 11(numerator )over2x^2-5x+2      Log On

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Question 295775: subtracting rational expressions having different denominators
I have a solution to this problem but I need to know if it is correct.

7x^2+15x- 11(numerator )over2x^2-5x+2(denominator) subtracted from -4x+5 (numerator)over x-2(denomintor )
Found 2 solutions by richwmiller, stanbon:
Answer by richwmiller(9143) About Me  (Show Source):
You can put this solution on YOUR website!
%28-4x%2B5%29%2F%28x-2%29-%287x%5E2%2B15x-+11%29%2F%282x%5E2-5x%2B2%29
%28-15+x%5E2-x%2B6%29%2F%28%28x-2%29+%282+x-1%29%29
Is this what you want?
What is your solution?
(2x^2-5x+2) factors to (x-2)*(2x-1)
or did you want this?
%287x%5E2%2B15x-+11%29%2F%282x%5E2-5x%2B2%29-%28-4x%2B5%29%2F%28x-2%29
%2815x%5E2%2Bx-6%29%2F%28%28x-2%29%2A%282x-1%29%29

Answer by stanbon(57410) About Me  (Show Source):
You can put this solution on YOUR website!
7x^2+15x- 11(numerator )over2x^2-5x+2(denominator) subtracted from -4x+5 (numerator)over x-2(denomintor )
-----------------
[7x^2+15x-11] / [2x^2-5x+2] - [-4x+5] / [x-2]
----------------------------------
Factor the denominator of the 1st fraction:
2x^2-5x+2
2x^2 -4x-x +2
2x(x-2)-(x-2)
(x-2)(2x-1)
----------------
So the least common denominator is (x-2)(2x-1)
-------------------
Rewrite each fraction with the lcd as its denominator:
[7x^2+15x-11]/lcd - [2x-1][-4x+5]/lcd
-----
Combine the numerators over the lcd:
[7x^2+15x-11-[-7x^2+10x+4x-5]]/lcd
-------------------------------------
Simplify:
[14x^2+29x-5]/[2x^2-5x+2]
================================
Cheers,
Stan H.
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