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Solve 5/(X - 2) - 3/(X + 6) = 4/X - Mathematics

Solve `5/(x - 2) -  3/(x + 6) = 4/x`

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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`

`=> 4x^2 + 16x - 48 = 2x^2 + 36`

`=> 2x^2 - 20x - 48 = 0`

`=> x^2 - 10x - 24 = 0`

`=> x^2 - 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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