SOLUTION: How do I solve a rational equation if I multiply the numerators by the lowest common denominators and several result in squared variables? The problem in question is: [x/(x+2)]+

Question 396898: How do I solve a rational equation if I multiply the numerators by the lowest common denominators and several result in squared variables?
The problem in question is: [x/(x+2)]+x=[(5x+8)/(x+2)]
The LCD appears to be x+2.
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
How do I solve a rational equation if I multiply the numerators by the lowest common denominators and several result in squared variables?
The problem in question is: [x/(x+2)]+x=[(5x+8)/(x+2)]
The LCD appears to be x+2.
The first step in solving this type of equation is to clear all the fractions so you will only be working with whole numbers.
You do this by first determine what the LCD is which you correctly identified as (x+2)
(x/(x+2))+x=(5x+8)/(x+2)
x+x(x+2)=(5x+8) (multiply all terms by (x+2) to rid of fractions)
x+x^2+2x=5x+8 (expand or distribute to get rid of parenthesis)
x^2-2x-8=0 (combine like terms and equate expression to zero)
This is a quadratic equation which can be solved by factoring or by the quadratic formula. Always try to factor first.
(x-4)(x+2)=0
answers: x=4 or x=-2
check for correctness by substituting x-values into the original equation.
4/(4+2)+4 = (20+8)/6 (substituting x=4)
14/3 = 28/6=14/3
try x=-2 (this answer has to be rejected because this would make two of the denominators = zero, which make the terms undefined.)

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