Answer:

The solution set is { -3 , 2 }

Explanation:

Since we are given that,

x/x+1 + x+1/x = 13/6

Lets say,

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

First we have to reduce it to standard form i-e, ax2+bx+C = 0

=>  multiplying both sides of eq 1 by ( x+1) , we get

= x + x+1(x+1)/x = 13/6 (x+1) ----------equation 2

=>now, multiplying both sides of eq 2 by x, we get

= x2 + x+1( x+1) = 13x/6 (x+1)

= x2 +x2+2x +1 = 13x2/6 + 13x/6

= 2X2 + 2x + 1 = 13x2 + 13x/6 ----------- equation 3

=> now multiplying both sides of eq 3 by 6. we get,

= 12x2 +12x + 6 = 13x2 + 13x

Now, subtracting terms of left hand sides on both sides to make it equal to zero.

=> 12x2 + 12x + 6 - 12x2 - 12x - 6 = 13x2 + 13x - 12x2 - 12x - 6

= 0 = x2 + x - 6

Rearranging the above equation.

=> x2 + x - 6 = 0 -------- equation 4.

So finally its a standard form of quadratic equation. Now comparing the values.

so here, a = 1 , B = 1 and c = -6

Quadratic Formula:    

x = -b+-√b2-4ac/ 2a

by putting the above values and ONE step calculation you will get these values.

x = -1 +-√1+24/2

x = -1 +- 5/2

so this MEANS,

x = -1 +5/2  or -1 -5/2

x =   4/2      or  -6/2

x =    2        or   -3

Result:

Hence the solution set is { -3 , 2 }

illustrations:

*  13/6 (x+1) means 13 /6 multiply by (x+1).

*  x2 means x square.

* 13x2/6 means 13x square with denominator 6

* Similarly, 12x2 means 12x square.

Hope this Answer the Question.

P.S: Sorry, but I myself like detailed answers. :)