Question
Answer
$$\dfrac{\dfrac{\dfrac{x}{4x-5}}{2x-5}}{1}=\dfrac{x}{8x^2-30x+25}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{\frac{\frac{x}{4x-5}}{2x-5}}{1}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{\frac{x}{8x^2-30x+25}}{1} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{x}{8x^2-30x+25}\end{aligned} $$ | |
| ① | Divide $ \dfrac{x}{4x-5} $ by $ 2x-5 $ to get $ \dfrac{x}{8x^2-30x+25} $. Step 1: To divide rational expressions, multiply the first fraction by the reciprocal of the second fraction. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{ \frac{x}{4x-5} }{2x-5} & \xlongequal{\text{Step 1}} \frac{x}{4x-5} \cdot \frac{\color{blue}{1}}{\color{blue}{2x-5}} \xlongequal{\text{Step 2}} \frac{ x \cdot 1 }{ \left( 4x-5 \right) \cdot \left( 2x-5 \right) } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ x }{ 8x^2-20x-10x+25 } = \frac{x}{8x^2-30x+25} \end{aligned} $$ |
| ② | Divide $ \dfrac{x}{8x^2-30x+25} $ by $ 1 $ to get $ \dfrac{ x }{ 8x^2-30x+25 } $. Step 1: To divide rational expressions, multiply the first fraction by the reciprocal of the second fraction. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{ \frac{x}{8x^2-30x+25} }{1} & \xlongequal{\text{Step 1}} \frac{x}{8x^2-30x+25} \cdot \frac{\color{blue}{1}}{\color{blue}{1}} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ x \cdot 1 }{ \left( 8x^2-30x+25 \right) \cdot 1 } \xlongequal{\text{Step 3}} \frac{ x }{ 8x^2-30x+25 } \end{aligned} $$ |
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Simplify Rational Expressions