Question

(x/x+1)+(x+1/x)=25/12

Answer 1

it has two values :
x=3
x=-4

Answer 2

Given,

($\frac{x}{x+1}$)+($\frac{x+1}{x}$)=$\frac{25}{12}$.

To Find,

The value of x.

Solution,

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

So we get,

$\frac{x^{2} +(x+1)^{2} }{x(x+1)}$=$\frac{25}{12}$.

⇒12×[$x^{2} +x^{2} +2x+1$]=25×[$x^{2} +x$].

⇒24$x^{2}$+24x+12=25$x^{2}$+25x.

⇒$x^{2}$+x-12=0

⇒$x^{2}$+4x-3x-12=0

⇒x(x+4)-3(x+4)=0

⇒(x-3)(x+4)=0.

⇒x=3 or x=-4,

Hence, the value of x is either 3 or -4.