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Solve (3x - 2)/(2x - 3) = (3x - 8)/(X + 4) - Mathematics

Solve `(3x - 2)/(2x - 3) = (3x - 8)/(x + 4)`

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Solution

`(3x - 2)/(2x - 3) = (3x - 8)/(x + 4)`

`=> (3x - 2)(x = 4) = (2x - 3)(3x - 8)`

`=> 3x^2 + 12x - 2x - 8 = 6x^2 -  16x - 9x + 24`

`=> 3x^2 + 10x - 8 = 6x^2 - 25x + 24`

`=> 3x^2 - 32x - 3x + 32 = 0`

=> x(3x - 32) - 1(3x - 32) = 0

=> (x - 1)(3x - 32) = 0

if x - 1 = 0 or 3x - 32 = 0

`=> x = 1  or  x = 32/3 = 10 2/3`

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