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5. \( \frac{x+1}{1+\frac{1}{x}} \)

Ask by Bryant Santiago. in the United States
Jan 22,2025

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Tutor-Verified Answer

Answer

The simplified form is \( x \).

Solution

Calculate or simplify the expression \( (x+1)/(1+1/x) \). Simplify the expression by following steps: - step0: Solution: \(\frac{\left(x+1\right)}{\left(1+\frac{1}{x}\right)}\) - step1: Remove the parentheses: \(\frac{x+1}{1+\frac{1}{x}}\) - step2: Add the terms: \(\frac{x+1}{\frac{x+1}{x}}\) - step3: Multiply by the reciprocal: \(\left(x+1\right)\times \frac{x}{x+1}\) - step4: Reduce the fraction: \(1\times x\) - step5: Multiply the terms: \(x\) The simplified form of the expression \( \frac{x+1}{1+\frac{1}{x}} \) is \( x \).

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Bonus Knowledge

To simplify the expression \( \frac{x+1}{1+\frac{1}{x}} \), you can start by rewriting the denominator. The term \( 1+\frac{1}{x} \) can be rewritten as \( \frac{x+1}{x} \) by getting a common denominator. Now the expression becomes: \[ \frac{x+1}{\frac{x+1}{x}} = (x+1) \cdot \frac{x}{x+1} = x \] So, the simplified form of the expression is \( x \). Enjoy that neat algebraic shortcut! It's a smooth ride once you get past the fraction.

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