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Question
Solve the following quadratic equations by factorization:
`5/(x - 2) - 3/(x + 6) = 4/x`
Solution
`5/(x - 2) - 3/(x + 6) = 4/x`
⇒ `(5(x + 6) - 3(x - 2))/((x - 2)(x + 6)) = 4/x`
⇒`(5x + 30 - 3x + 6)/(x^2 + 6x - 2x - 12) = 4/x`
⇒ `(2x + 36)/(x^2 + 4x - 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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