Question 465534
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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