Tap the blue circles to see an explanation.
$$ \begin{aligned}\frac{\frac{5}{4}}{\frac{5}{m}-\frac{4}{m}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{\frac{5}{4}}{\frac{1}{m}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{5m}{4}\end{aligned} $$ | |
① | To subtract expressions with the same denominators, we subtract the numerators and write the result over the common denominator. $$ \begin{aligned} \frac{5}{m} - \frac{4}{m} & = \frac{5}{\color{blue}{m}} - \frac{4}{\color{blue}{m}} =\frac{ 5 - 4 }{ \color{blue}{ m }} = \\[1ex] &= \frac{1}{m} \end{aligned} $$ |
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. $$ \begin{aligned} \frac{ \frac{5}{4} }{ \frac{\color{blue}{1}}{\color{blue}{m}} } & \xlongequal{\text{Step 1}} \frac{5}{4} \cdot \frac{\color{blue}{m}}{\color{blue}{1}} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ 5 \cdot m }{ 4 \cdot 1 } \xlongequal{\text{Step 3}} \frac{ 5m }{ 4 } \end{aligned} $$ |