Question

3/x-1 + 1/x-3 = 4/x-2​

Answer 1

$\underline{\underline{\huge{\pink{\tt{\textbf Answer :-}}}}}$

$\frac{3}{x + 1} + \frac{1}{x - 3} = \frac{4}{x - 2}$

$\frac{3(x - 3) + x + 1}{(x + 1)(x - 3)} = \frac{4}{x - 2}$

$\frac{3x - 9 + x + 1}{ {x}^{2} - 3x + x - 3 } = \frac{4}{x - 2}$

$\frac{4x - 8}{ {x}^{2} - 2x - 3 } = \frac{4}{x - 2}$

$4 {x}^{2} - 8x - 8x + 16 = 4 {x}^{2} - 8x - 12$

-8x=-12-16

-8x=-28

x=3.5

Answer 2

$\frac{3}{x - 1} + \frac{1}{x - 3} = \frac{4}{x - 2}$

$\frac{3(x - 3) + (x - 1)}{(x - 1)(x - 3)} = \frac{4}{x - 2}$

$\frac{3x - 9 + x - 1}{x(x - 3) - 1(x - 3)} = \frac{4}{x - 2}$

$\frac{4x - 10}{ {x}^{2} - 3x - x + 3 } = \frac{4}{x - 2}$

$\frac{4x - 10}{ {x}^{2} - 4x + 3 } = \frac{4}{x - 2}$

$(4x - 10)(x - 2) = {x}^{2} - 4x + 3(4)$

$4 {x}^{2} - 8x - 10x + 20 = {x}^{2} - 4x + 12 \\ 3 {x}^{2} - 18x + 20 = - 4x + 12 \\ 3 {x}^{2} - 14x + 8 = 0$