Question

Solve for x: x/x-1+x-1/x=4

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Given,

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

To Find,

The value of x.

Solution,

We need to simplify the ($\frac{x}{x-1}$)+($\frac{x-1}{x}$) first.

So we get,

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

⇒$\frac{x^{2}+(x-1)^{2} }{x(x-1)}$=4.

⇒$\frac{2x^{2} -2x+1}{x^{2} -x}$=4.

⇒2$x^{2}$-2x+1=4$x^{2}$-4x.

⇒2$x^{2}$-2x-1=0.

Apply Sri Dhar acharya's law to solve,

So, x = $\frac{[-(-2)+\sqrt{4-4.2.(-1)} ]}{2.2}$ or x =$\frac{[-(-2)-\sqrt{4-4.2.(-1)} ]}{2.2}$

⇒x=$\frac{[2+\sqrt{12} ]}{4}$ or x =$\frac{[2-\sqrt{12} ]}{4}$

⇒x=$\frac{[1+\sqrt{3} ]}{2}$ or x= $\frac{[1-\sqrt{3} ]}{2}$.

Hence, the value of x is either $\frac{[1+\sqrt{3} ]}{2}$ or $\frac{[1-\sqrt{3} ]}{2}$