Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{4}{x}+\frac{\frac{1}{4}}{x}-1& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(4+\frac{1}{4})\cdot\frac{1}{x}-1 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{17}{4}\cdot\frac{1}{x}-1 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{17}{4x}-1 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{-4x+17}{4x}\end{aligned} $$ | |
| ① | Use the distributive property. |
| ② | Combine like terms |
| ③ | Multiply $ \dfrac{17}{4} $ by $ \dfrac{1}{x} $ to get $ \dfrac{ 17 }{ 4x } $. Step 1: Multiply numerators and denominators. Step 2: Simplify numerator and denominator. $$ \begin{aligned} \frac{17}{4} \cdot \frac{1}{x} \xlongequal{\text{Step 1}} \frac{ 17 \cdot 1 }{ 4 \cdot x } \xlongequal{\text{Step 2}} \frac{ 17 }{ 4x } \end{aligned} $$ |
| ④ | Subtract $1$ from $ \dfrac{17}{4x} $ to get $ \dfrac{ \color{purple}{ -4x+17 } }{ 4x }$. Step 1: Write $ 1 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: To subtract raitonal expressions, both fractions must have the same denominator. |