Question

solve (2x+3/x+1)+6(x+1/2x+3)-7=0

Answer 1

((2x + 3)/(x + 1)) + 6((x + 1)/(2x + 3)) - 7 = 0

Let

y = (2x + 3)/(x + 1) ——> 1

1/y = (x + 1)/(2x + 3)

y + 6*(1/y) - 7 = 0

y^2 - 7y + 6 = 0

y^2 - y - 6y + 6 = 0

y(y - 1) - 6(y - 1) = 0

(y - 1)(y - 6) = 0

y - 1 = 0, y - 6 = 0

y = 1, 6 ——-> 2

Substitute y = 1 & 6 in equation 1,

When y = 1,

1 = (2x + 3)/(x + 1)

x + 1 = 2x + 3

2x - x = 1 - 3

x = -2

When y = 6,

6 = (2x + 3)/(x + 1)

6(x + 1) = (2x + 3)

6x + 6 = 2x + 3

6x - 2x = 3 - 6

4x = -3

x = -3/4

Therefore x = -2, -3/4 ——> Answer