Question

1/x + x/x+1 is equivalent to

Answer 1

To simplify the expression \( \frac{1}{x} + \frac{x}{x+1} \), we can start by finding a common denominator, which would be \( x(x+1) \).

1. Rewrite each term with the common denominator:

\[
\frac{1}{x} = \frac{1(x+1)}{x(x+1)} = \frac{x+1}{x(x+1)}
\]

\[
\frac{x}{x+1} = \frac{x \cdot x}{(x+1) \cdot x} = \frac{x^2}{x(x+1)}
\]

2. Now, we can combine the two fractions:

\[
\frac{x+1}{x(x+1)} + \frac{x^2}{x(x+1)} = \frac{(x + 1) + x^2}{x(x + 1)} = \frac{x^2 + x + 1}{x(x + 1)}
\]

So, the simplified form of \( \frac{1}{x} + \frac{x}{x+1} \) is

\[
\frac{x^2 + x + 1}{x(x + 1)}
\]