Solve x/(x+1)-1/2=-1/(x+1)?

Question

A) 1
B) no solution
C) 0
D) -1

Answer 1

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

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

Cancel the term x + 1 to each side

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

Simplify

x -1 / 2 = -1

Multiply each side by 2

x - 1 = -2

x = -1

D is the right choice.

Comments

Cross check the solution by substituting x = -1 in the expression
 -1 / (-1 + 1) - 1 / 2 = -1 / (-1 + 1)
 -1 / 0 - 1 / 2 = -1 / 0

Since denominator is zero, no solution exists.

Option B is right choice.