Question

What do we get on simplifying the expression $\frac{x}{x+1}+\frac{x+1}{x}-\frac{1}{x(x+1)}$ ?

• A. x/2
• B. x
• C. 1/2
• D. 2

Answer 1

Answer:

D. 2

$\frac{x}{x+1}+\frac{x+1}{x}-\frac{1}{x(x+1)}$

$\frac{x\times x}{x(x+1}+\frac{(x+1)(x+1)}{x(x+1)}-\frac{1}{x(x+1)}$

$\frac{x^2+(x+1)^2-1}{x(x+1)}$

$\frac{x^2+x^2+2x+1-1}{x(x+1)}$

$\frac{x(x+x+2)}{x(x+1)}$

$\frac{2x+2}{x+1}$

$2(x+1){x+1}$

=2