Question

solve 3x+1/x+1 +x+1/3x+1=5\2

Answer 1

Given;
{(3x+1)/(x+1)}+{(x+1)/(3x+1)} = 5/2 

[(3x + 1)^2 + (x + 1)^2]/(3x+1)(x+1) = 5/2

(10x^2 + 8x + 2)/(3x^2 + 4x + 1) = 5/2

20x^2 + 16x +4 = 15x^2 +20x + 5

5x^2 - 4x -1 = 0

5x^2 -(5 - 1)x = 0

5x^2 - 5x + x - 1 = 0

5x(x - 1) + 1(x - 1) = 0

5x + 1 = 0
x = -1/5
or

x -1 = 0
x = 1

so answer will be 1,-1/5(option 3)