Question

solve the equation to find x
1/(x-1) + 3/(x+1) = 4/x

Please help me if you know the answer ​

Answer 1

Step-by-step explanation:

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

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

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

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

$4( {x}^{2} - 1) = x(4x - 2)$

$4 {x}^{2} - 4 = 4 {x}^{2} - 2x$

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

$2x - 4 = 0$

$2x = 4$

$x = \frac{4}{2}$

$x = 2$

The value of x is 2.

Answer 2

1 + 3 = 4

(x-1) (x+1) x

1(x+1) + 3(x-1) = 4

(x-1)(x+1) x

x+1 + 3x-3 = 4

(x²-1) x

4x-2 = 4

(x²-1) x

(4x-2)x = 4(x²-1)

4x²-2x = 4x²-4

4x²-4x² -2x = -4

-2x = -4

x = -4

-2

x = 2