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Question
Solve the following quadratic equations by factorization:
`(x-3)/(x+3)-(x+3)/(x-3)=48/7` , x ≠ 3, x ≠ -3
Solution
We have been given
`(x-3)/(x+3)-(x+3)/(x-3)=48/7`
7(x2 + 9 - 6x - x2 - 9 - 6x) = 48(x2 - 9)
48x2 + 84x - 432 = 0
4x2 + 7x - 36 = 0
Therefore,
4x2 + 16x - 9x - 36 = 0
4x(x + 4) - 9(x + 4) = 0
(4x - 9)(x + 4) = 0
Therefore,
4x - 9 = 0
4x = 9
x = 9/4
or,
x + 4 = 0
x = -4
Hence, x = 9/4 or x = -4.
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