Write the following as a single rational expression

Ask by Hill Warren. in the United States

Jan 26,2025

Question

Write the following as a single rational expression $$ \frac{1}{x-1}-\frac{1}{x} $$

UpStudy AI · Accepted Answer

Calculate or simplify the expression $$ \frac{1}{x-1}-\frac{1}{x} $$.
Simplify the expression by following steps:
- step0: Solution:
  $$\frac{1}{x-1}-\frac{1}{x}$$
- step1: Reduce fractions to a common denominator:
  $$\frac{x}{\left(x-1\right)x}-\frac{x-1}{x\left(x-1\right)}$$
- step2: Rewrite the expression:
  $$\frac{x}{\left(x-1\right)x}-\frac{x-1}{\left(x-1\right)x}$$
- step3: Transform the expression:
  $$\frac{x-\left(x-1\right)}{\left(x-1\right)x}$$
- step4: Subtract the terms:
  $$\frac{1}{\left(x-1\right)x}$$
- step5: Multiply the terms:
  $$\frac{1}{x^{2}-x}$$
The given expression $$ \frac{1}{x-1}-\frac{1}{x} $$ can be simplified to $$ \frac{1}{x^{2}-x} $$.
The expression simplifies to $$ \frac{1}{x^{2}-x} $$.

Write the following as a single rational expression

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