Question

Solve x/x+1+x+1/x=13/6
​

Answer 1

Answer:

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}

x−1

x

+

x

x−1

=

6

13

To find : Solve the expression ?

Solution :

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

x−1

x

+

x

x−1

=

6

13

Taking LCM,

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

x(x−1)

x

2

+(x−1)

2

=

6

13

Cross multiply,

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

2

+6(x

2

+1−2x)=13x(x−1)

Open the bracket,

6x^2+6x^2+6-12x=13x^2-13x6x

2

+6x

2

+6−12x=13x

2

−13x

Take like term together,

x^2-x-6=0x

2

−x−6=0

Solve by middle term split,

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

2

−3+2x−6=0

x(x-3)+2(x-3)=0x(x−3)+2(x−3)=0

(x-3)(x+2)=0(x−3)(x+2)=0

x=3,-2x=3,−2

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