Question #N244
The expression $\frac{1}{x} - \frac{1}{x+1}$ is equivalent to which of the following?
A. $\frac{1}{x^2 + x}$
B. $\frac{1}{x^2 + 1}$
C. $\frac{1}{x(x+1)}$
D. $\frac{1}{x(x-1)}$
Correct Answer is: C
To combine the fractions, we need a common denominator. The common denominator is $x(x+1)$. Multiplying the first fraction by $\frac{x+1}{x+1}$ and the second fraction by $\frac{x}{x}$ gives $\frac{x+1}{x(x+1)} - \frac{x}{x(x+1)}$. Combining the numerators, we get $\frac{x + 1 - x}{x(x+1)}$, which simplifies to $\frac{1}{x(x+1)}$.