Question

solve x/x-1 + x-1/x = 13/6

Answer 1

the answer is given in the picture.

Answer 2

Answer:

The solution of the expression is x=3,-2.

Step-by-step explanation:

Given : Expression $\frac{x}{x-1}+\frac{x-1}{x}=\frac{13}{6}$

To find : Solve the expression ?

Solution :

Expression $\frac{x}{x-1}+\frac{x-1}{x}=\frac{13}{6}$

Taking LCM,

$\frac{x^2+(x-1)^2}{x(x-1)}=\frac{13}{6}$

Cross multiply,

$6x^2+6(x^2+1-2x)=13x(x-1)$

Open the bracket,

$6x^2+6x^2+6-12x=13x^2-13x$

Take like term together,

$x^2-x-6=0$

Solve by middle term split,

$x^2-3+2x-6=0$

$x(x-3)+2(x-3)=0$

$(x-3)(x+2)=0$

$x=3,-2$

Therefore, The solution of the expression is x=3,-2.