Math Calculators, Lessons and Formulas

It is time to solve your math problem

mathportal.org

◀ back to index

Question

Answer

$$\dfrac{1}{x}-\dfrac{1}{1+1}=\dfrac{-x+2}{2x}$$

Explanation

Tap the blue circles to see an explanation.

$$ \begin{aligned}\frac{1}{x}-\frac{1}{1+1}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{1}{x}-\frac{1}{2} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{-x+2}{2x}\end{aligned} $$
①

Simplify denominator

$$ \color{blue}{1} + \color{blue}{1} = \color{blue}{2} $$
②

Subtract $ \dfrac{1}{2} $ from $ \dfrac{1}{x} $ to get $ \dfrac{ \color{purple}{ -x+2 } }{ 2x }$.

To subtract raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the first fraction by $ \color{blue}{ 2 }$ and the second by $\color{blue}{ x }$.

$$ \begin{aligned} \frac{1}{x} - \frac{1}{2} & = \frac{ 1 \cdot \color{blue}{ 2 }}{ x \cdot \color{blue}{ 2 }} - \frac{ 1 \cdot \color{blue}{ x }}{ 2 \cdot \color{blue}{ x }} = \\[1ex] &=\frac{ \color{purple}{ 2 } }{ 2x } - \frac{ \color{purple}{ x } }{ 2x }=\frac{ \color{purple}{ -x+2 } }{ 2x } \end{aligned} $$
This page was created using
Simplify Rational Expressions