Question

solve the following equation.​

Answer 1

Answer:

$x = 3$

Step-by-step explanation:

$\frac{1}{x - 1} + \frac{2}{x + 1} = \frac{3}{x} \\ \frac{1(x + 1) + 2(x - 1)}{(x - 1)(x + 1)} = \frac{3}{x} \\ \frac{x + 1 + 2x - 2}{ {x}^{2} - 1} = \frac{3}{x} \\ \frac{x + 2x + 1 - 2}{ {x}^{2} - 1 } = \frac{3}{x} \\ \frac{3x - 1}{ {x}^{2} - 1 } = \frac{3}{x} \\ cross \: multiply \\ 3( {x}^{2} - 1) = x(3x - 1) \\ 3 {x}^{2} - 3 = 3 {x}^{2} - x \\3 {x}^{2} - 3 {x}^{2} + x - 3 = 0 \\ x - 3 = 0 \\ x = 3$

Answer 2

Answer:

x=3/2

Step-by-step explanation:

(1/x-1)+(2/x+1)=3/x

now taking LCM ....

{1(x+1)+ 2(x-1)}/(x-1)(x+1)=3/x

we know that a²-b²=(a+b)(a-b) so ,

x+1+2x-2/(x²-1²)=3/x

3x-2/x²-1=3/x

3x-2=3/x × (x²-1)

3x-2= 3x-3/x

now,3x get cancelled out ....

-2=-3/x

minus also get cancelled

2x=3

so....

x=3/2