Tap the blue circles to see an explanation.
$$ \begin{aligned}\frac{\frac{\frac{4x-8}{x^2-5x+6}}{8x+48}}{x^2+3x-18}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{\frac{\frac{4}{x-3}}{8x+48}}{x^2+3x-18} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{\frac{4}{8x^2+24x-144}}{x^2+3x-18} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{4}{8x^4+48x^3-216x^2-864x+2592}\end{aligned} $$ | |
① | Factor both the denominator and the numerator, then cancel the common factor. $\color{blue}{x-2}$. $$ \begin{aligned} \frac{4x-8}{x^2-5x+6} & =\frac{ 4 \cdot \color{blue}{ \left( x-2 \right) }}{ \left( x-3 \right) \cdot \color{blue}{ \left( x-2 \right) }} = \\[1ex] &= \frac{4}{x-3} \end{aligned} $$ |
② | 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. $$ \begin{aligned} \frac{ \frac{4}{x-3} }{8x+48} & \xlongequal{\text{Step 1}} \frac{4}{x-3} \cdot \frac{\color{blue}{1}}{\color{blue}{8x+48}} \xlongequal{\text{Step 2}} \frac{ 4 \cdot 1 }{ \left( x-3 \right) \cdot \left( 8x+48 \right) } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 4 }{ 8x^2+48x-24x-144 } = \frac{4}{8x^2+24x-144} \end{aligned} $$ |
③ | 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. $$ \begin{aligned} \frac{ \frac{4}{8x^2+24x-144} }{x^2+3x-18} & \xlongequal{\text{Step 1}} \frac{4}{8x^2+24x-144} \cdot \frac{\color{blue}{1}}{\color{blue}{x^2+3x-18}} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ 4 \cdot 1 }{ \left( 8x^2+24x-144 \right) \cdot \left( x^2+3x-18 \right) } \xlongequal{\text{Step 3}} \frac{ 4 }{ 8x^4+24x^3-144x^2+24x^3+72x^2-432x-144x^2-432x+2592 } = \\[1ex] &= \frac{4}{8x^4+48x^3-216x^2-864x+2592} \end{aligned} $$ |