Solve$\frac{3}{x+1} -\frac{2}{3x-1} = \frac{1}{2}$

Given: $\frac{3}{x+1} -\frac{2}{3x-1} = \frac{1}{2}$

To do: Solve for $x$.

Solution:

$\frac{3}{x+1} -\frac{2}{3x-1} = \frac{1}{2}$

$\frac{3(3x-1)-2(x+1)}{(x+1)(3x-1)} = \frac{1}{2}$

$2[9x - 3 -2x -2] = (x+1)(3x-1)$

$2(7x-5) = 3x^{2} +3x - x - 1$

$14x - 10 = 3x^{2} + 2x -1$

$3x^{2} -12x + 9 = 0$

$x^{2} -4x + 3 = 0$

$(x -3)(x-1) =0$

So $x$ = 1, 3  Answer

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Updated on: 10-Oct-2022

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