SOLUTION: Can you help me solve the equation by using the Lowest Common Denominator? The problem is 5/x^2+x-6 = 2+ x-3/x-2 Can you show me step by step how to get the answer? My teacher

Algebra ->  Rational-functions -> SOLUTION: Can you help me solve the equation by using the Lowest Common Denominator? The problem is 5/x^2+x-6 = 2+ x-3/x-2 Can you show me step by step how to get the answer? My teacher      Log On


   

Question 413652: Can you help me solve the equation by using the Lowest Common Denominator? The problem is
5/x^2+x-6 = 2+ x-3/x-2
Can you show me step by step how to get the answer? My teacher can't teach and the homework hotline is closed.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
5%2F%28x%5E2%2Bx-6%29 = 2 + %28x-3%29%2F%28x-2%29
Factor the 1st denominator
5%2F%28%28x%2B3%29%28x-2%29%29 = 2 + %28x-3%29%2F%28x-2%29
the common denominator consists of the factors of both denominators
the common denominator is (x+3)(x-2)*
Multiply each term by the common denominator
(x+3)(x-2)*5%2F%28%28x%2B3%29%28x-2%29%29 = (x+3)(x-2)*2 + (x+3)(x-2)*%28x-3%29%2F%28x-2%29
Cancel out the denominators that you can and you have:
5 = 2(x+3)(x-2) + (x+3)(x-3)
FOIL
5 = 2(x^2 - 2x + 3x - 6) + (x^2 -3x + 3x - 9)
5 = 2(x^2 + x - 6) + (x^2-9)
5 = 2x^2 + 2x - 12 + x^2 - 9
Combine like terms
0 = 2x^2 + x^2 + 2x - 12 - 9 - 5
a quadratic equation
3x^2 + 2x - 26 = 0
You have to solve this equation using the quadratic formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
In this equation; a=3; b=2; c=-26
x+=+%28-2+%2B-+sqrt%282%5E2-4%2A3%2A-26+%29%29%2F%282%2A3%29+
x+=+%28-2+%2B-+sqrt%284-%28-312%29+%29%29%2F%286%29+
x+=+%28-2+%2B-+sqrt%284+%2B+312+%29%29%2F%286%29+
x+=+%28-2+%2B-+sqrt%28316+%29%29%2F%286%29+
Two solutions
x+=+%28-2+%2B+17.776%29%2F%286%29+
x = 15.776%2F6
x = 2.63
and
x+=+%28-2+-+17.776%29%2F%286%29+
x = 19.776%2F6
x = -3.296
:
You job is to check both these solutions in the original equation