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.Com
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) (Show Source): You can put this solution on YOUR website!
= 2 +
Factor the 1st denominator
= 2 +
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)* = (x+3)(x-2)*2 + (x+3)(x-2)*
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
In this equation; a=3; b=2; c=-26
Two solutions
x =
x = 2.63
and
x =
x = -3.296
:
You job is to check both these solutions in the original equation
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