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Question
Solve the following quadratic equations by factorization:
`(x+3)/(x+2)=(3x-7)/(2x-3)`
Solution
We have been given
`(x+3)/(x+2)=(3x-7)/(2x-3)`
2x2 - 3x + 6x - 9 = 3x2 - 7x + 6x - 14
x2 - 4x - 5 = 0
x2 - 5x + x - 5 = 0
x(x - 5) + 1(x - 5) = 0
(x + 1)(x - 5) = 0
Therefore,
x + 1 = 0
x = -1
or,
x - 5 = 0
x = 5
Hence, x = -1 or x = 5
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