Questions: 1/x + x/(2x)

Solution Steps

To simplify the given expression, we need to combine the fractions by finding a common denominator. Then, we can add the numerators and simplify the resulting fraction.

1. Identify the common denominator for the fractions.
2. Rewrite each fraction with the common denominator.
3. Add the numerators.
4. Simplify the resulting fraction if possible.

To add the fractions \(\frac{1}{x}\) and \(\frac{x}{2x}\), we first identify the common denominator. The common denominator for \(x\) and \(2x\) is \(2x\).

Rewrite each fraction with the common denominator \(2x\): \[ \frac{1}{x} = \frac{2}{2x} \] \[ \frac{x}{2x} = \frac{1}{2} \]

Now, add the numerators: \[ \frac{2}{2x} + \frac{1}{2} = \frac{2 + x}{2x} \]

The resulting fraction is already in its simplest form: \[ \frac{2 + x}{2x} \]

Final Answer