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Question
Solve equation using factorisation method:
`5/("x" -2) - 3/("x" + 6) = 4/"x"`
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Solution
`5/("x" -2) - 3/("x" + 6) = 4/"x"`
⇒ `(5("x" + 6) -3("x" -2))/(("x" -2)("x" + 6)) = 4/"x"`
⇒ `(5"x" + 30 - 3"x" + 6)/("x"^2 + 6"x" - 2"x" - 12) = 4/"x"`
⇒ `(2"x" + 36)/("x"^2 + 4"x" - 12) = 4/"x"`
⇒ 4x2 + 16x - 48 = 2x2 + 36x
⇒ 2x2 - 20x - 48 = 0
⇒ x2 - 10x - 24 = 0
⇒ x2 - 12x + 2x - 24 = 0
⇒ x(x - 12) + 2(x - 12) = 0
⇒ (x - 12) (x + 2) = 0
If x - 12 = 0 or x + 2 = 0
then x = 12 or x = -2
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