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Question
Solve the following equation by factorization
`(x + 2)/(x + 3) = (2x - 3)/(3x - 7)`
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Solution
`(x + 2)/(x + 3) = (2x - 3)/(3x - 7)`
(x + 2) (3x - 7) = (2x - 3) (x + 3)
⇒ 3x2 - 7x + 6x - 14 = 2x2 + 6x - 3x - 9
⇒ 3x2 - x - 14 = 2x2 + 3x - 9
⇒ 3x2 - x - 14 - 2x2 - 3x + 9 =0
⇒ x2 - 4x - 5 = 0
⇒ x2 - 5x + x - 5 = 0
x(x - 5) + 1(x - 5) = 0
⇒ (x - 5) (x + 1) = 0
Either x - 5 = 0,
then x = 5
or
x + 1 = 0,
then x = -1
Hence x = 5, -1.
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