SOLUTION: I am confused on how to solve this problem 3a/a^2-2a-15 -a/a+3=2a/a-5 I am trying to figure out solving Equations Containing Rational Expressions. I can't figure this out caus

Algebra ->  Radicals -> SOLUTION: I am confused on how to solve this problem 3a/a^2-2a-15 -a/a+3=2a/a-5 I am trying to figure out solving Equations Containing Rational Expressions. I can't figure this out caus      Log On


   

Question 465534: I am confused on how to solve this problem
3a/a^2-2a-15 -a/a+3=2a/a-5
I am trying to figure out solving Equations Containing Rational Expressions. I can't figure this out cause all are fractions.
Thanks
Answer by algebrahouse.com(1659) About Me  (Show Source):
You can put this solution on YOUR website!
First, you have to make sure everything is completely factored.

Then, you have to eliminate the fractions by multiplying the entire equation by the least common denominator.

3a/(aČ - 2a - 15) - a/(a + 3) = 2a/(a - 5)
3a/(a + 3)(a - 5) - a/(a + 3) = 2a/(a - 5) {factored denominator of 1st term}

Multiply the entire equation by the least common denominator:
[(a + 3)(a - 5)] [3a/(a + 3)(a - 5) - a/(a + 3) = 2a/(a - 5)]

Multiply each term by the common denominator:
(a + 3)(a - 5)[3a/(a + 3)(a - 5)] - (a + 3)(a - 5)[a/(a + 3)] = (a + 3)(a - 5)[2a/(a - 5)]

3a - a(a - 5) = 2a(a + 3) {cancelled and multiplied what's left}
3a - aČ + 5a = 2aČ + 6a {used distributive property}
-aČ + 8a = 2aČ + 6a {combined like terms}
3aČ - 2a = 0 {added aČ and subtracted 8a from both sides}\
a(3a - 2) = 0 {factored a out}
a = 0 or 3a - 2 = 0 {set each factor equal to 0}
a = 0 or 3a = 2 {added 2 to both sides in right equation}
a = 0 or a = 2/3 {divided both sides by 3 in right equation}
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