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Simplifying rational expressions
This solver simplifies rational expressions. This calculator factor both the numerator and denominator completely then reduce the expression by canceling common factors. Able to display the work process, and the detailed explanation. $$\frac{x^2+1}{2x^2-4x+2} ~ + ~\frac{x}{(x-1)^2} - \frac{x+1}{x^2-2x+1}$$
solution
$$9\cdot\frac{x^2}{36x^2-180x}=\frac{9x^2}{36x^2-180x}$$explanation
| $$ \begin{aligned}9 \cdot \frac{x^2}{36x^2-180x}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{9x^2}{36x^2-180x}\end{aligned} $$ | |
| ① | Multiply $9$ by $ \dfrac{x^2}{36x^2-180x} $ to get $ \dfrac{ 9x^2 }{ 36x^2-180x } $. Step 1: Write $ 9 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 9 \cdot \frac{x^2}{36x^2-180x} & \xlongequal{\text{Step 1}} \frac{9}{\color{red}{1}} \cdot \frac{x^2}{36x^2-180x} \xlongequal{\text{Step 2}} \frac{ 9 \cdot x^2 }{ 1 \cdot \left( 36x^2-180x \right) } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 9x^2 }{ 36x^2-180x } \end{aligned} $$ |
1. Simplifying Rational Expressions - purplemath.
2. Rational Expressions Tutorial — evaluate and simplify rational Expressions.
3. Rational Expressions — practice problems on Pauls online notes.