SOLUTION: FOR FUNMATH, sorry about the last problem but my instructer gave out the wrong question. The new problem is 6/x-2 + 7/x^2-4 = x+3/x+2 Please lean a hand, I'm getting mixed up.

Algebra ->  Algebra  -> Polynomials-and-rational-expressions -> SOLUTION: FOR FUNMATH, sorry about the last problem but my instructer gave out the wrong question. The new problem is 6/x-2 + 7/x^2-4 = x+3/x+2 Please lean a hand, I'm getting mixed up.      Log On

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Question 62876This question is from textbook Intermediate Algebra 9th
: FOR FUNMATH, sorry about the last problem but my instructer gave out the wrong question. The new problem is
6/x-2 + 7/x^2-4 = x+3/x+2
Please lean a hand, I'm getting mixed up.This question is from textbook Intermediate Algebra 9th

Found 3 solutions by Earlsdon, stanbon, funmath:
Answer by Earlsdon(6103) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x:
6%2F%28x-2%29+%2B+7%2F%28x%5E2-4%29+=+%28x%2B3%29%2F%28x%2B2%29 To simplify the left side, find the common denominator then add the fractions.
The common denominator can be found by first factoring the denominator of the second fraction: %28x%5E2-4%29+=+%28x-2%29%28x%2B2%29, so now you have:
6%2F%28x-2%29+%2B+7%2F%28%28x-2%29%28x%2B2%29%29+=+%28x%2B3%29%2F%28x%2B2%29 Now multiply the top & bottom of the first fraction by (x+2) then add the fractions:
%286%28x%2B2%29+%2B+7%29%2F%28x-2%29%28x%2B2%29+=+%28x%2B3%29%2F%28x%2B2%29 Now multiply both sides by (x+2) and cancel where appropriate.
%28x%2B2%29%286%28x%2B2%29%2B+7%29%2F%28x-2%29%28x%2B2%29+=+%28x%2B2%29%28x%2B3%29%2F%28x%2B2%29 After cancelling the (x+2)'s, and a little simplifying you have:
%28%286x%2B12%29%2B7%29%2F%28x-2%29+=+%28x%2B3%29 Multiply both sides by (x-2)
6x%2B12%2B7+=+%28x%2B3%29%28x-2%29 Simplify:
6x%2B19+=+x%5E2%2Bx-6
x%5E2-5x-25+=+0 Solve this quadratic equation using the quadratic formula: x+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a
x+=+%28-%28-5%29%2B-sqrt%28%28-5%29%5E2-4%281%29%28-25%29%29%29%2F2%281%29
x+=+%285%2B-sqrt%2825-%28-100%29%29%29%2F2
x+=+%285%2B-sqrt%28125%29%29%2F2
x+=+5%2F2%2B%285sqrt%285%29%29%2F2 = %285%2F2%29%281%2Bsqrt%285%29%29
x+=+5%2F2-%285sqrt%285%29%29%2F2 = %285%2F2%29%281-sqrt%285%29%29

Answer by stanbon(48568) About Me  (Show Source):
You can put this solution on YOUR website!
6/x-2 + 7/x^2-4 = (x+3)/(x+2)
----------
The LCM is (x-2)(x+2) or x^2-4
---------
Multiply thru by the LCM to get:
6(x+2)+7 = (x+3)(x-2)
6x+19=x^2+x-6
x^2-5x-25=0
x=[5+-sqrt(25-4(-25)]/2
x=[5+-5sqrt5]/2
x=(5/2)(1+sqrt5) or x=(5/2)(1-sqrt5)
Cheers,
Stan H.

Answer by funmath(2873) About Me  (Show Source):
You can put this solution on YOUR website!
This one is much more do-able!!!
6%2F%28x-2%29%2B7%2F%28x%5E2-4%29=%28x%2B3%29%2F%28x%2B2%29 First factor
6%2F%28x-2%29%2B7%2F%28%28x-2%29%28x%2B2%29%29=%28x%2B3%29%2F%28x%2B2%29
The LCD is (x-2)(x+2), the restricted values are x not= =\-2 (No 0 in denominator.) Multiply everything byt the LCD and the denominators melt away.
6%28x-2%29%28x%2B2%29%2F%28x-2%29%2B7%28x-2%29%28x%2B2%29%2F%28%28x-2%29%28x%2B2%29%29=%28x%2B3%29%28x-2%29%28x%2B2%29%2F%28x%2B2%29
6%2Across%28%28x-2%29%29%28x%2B2%29%2Fcross%28%28x-2%29%29%2B7%2Across%28%28x-2%29%28x%2B2%29%29%2Fcross%28%28x-2%29%28x%2B2%29%29=%28x%2B3%29%28x-2%29%2Across%28%28x%2B2%29%29%2Fcross%28%28x%2B2%29%29
6%28x%2B2%29%2B7=%28x%2B3%29%28x-2%29
6x%2B12%2B7=x%5E2-2x%2B3x-6
6x%2B19=x%5E2%2Bx-6
6x-6x%2B19-19=x%5E2%2Bx-6x-6-19
0=x%5E2-5x-25
The Quadratic formula ishighlight%28x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a%29
a=1, b=-5, and c=-25
x=%28-%28-5%29%2B-sqrt%28%28-5%29%5E2-4%281%29%28-25%29%29%29%2F%282%281%29%29
x=%285%2B-sqrt%2825%2B100%29%29%2F2
x=%285%2B-sqrt%28125%29%29%2F2
x=%285-sqrt%2825%29%2Asqrt%285%29%29%2F2 and x=%285%2Bsqrt%2825%29%2Asqrt%285%29%29%2F2
x=%285-5%2Asqrt%285%29%29%2F2 and x=%285%2B5%2Asqrt%285%29%29%2F2
x~~-3.090169944 and x~~8.090169944
Check the answers in your calculator in the original equation and you'll see they both work.
Happy Calculating!!!