Multiply $qrst$ by $ \dfrac{3}{2} $ to get $ \dfrac{ 3qrst }{ 2 } $.

Step 1: Write $ qrst $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} qrst \cdot \frac{3}{2} & \xlongequal{\text{Step 1}} \frac{qrst}{\color{red}{1}} \cdot \frac{3}{2} \xlongequal{\text{Step 2}} \frac{ qrst \cdot 3 }{ 1 \cdot 2 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 3qrst }{ 2 } \end{aligned} $$

Multiply $qrst$ by $ \dfrac{3}{2} $ to get $ \dfrac{ 3qrst }{ 2 } $.

Step 1: Write $ qrst $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} qrst \cdot \frac{3}{2} & \xlongequal{\text{Step 1}} \frac{qrst}{\color{red}{1}} \cdot \frac{3}{2} \xlongequal{\text{Step 2}} \frac{ qrst \cdot 3 }{ 1 \cdot 2 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 3qrst }{ 2 } \end{aligned} $$

Multiply $i$ by $ \dfrac{3qrst}{2} $ to get $ \dfrac{ 3iqrst }{ 2 } $.

Step 1: Write $ i $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} i \cdot \frac{3qrst}{2} & \xlongequal{\text{Step 1}} \frac{i}{\color{red}{1}} \cdot \frac{3qrst}{2} \xlongequal{\text{Step 2}} \frac{ i \cdot 3qrst }{ 1 \cdot 2 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 3iqrst }{ 2 } \end{aligned} $$

Multiply $i$ by $ \dfrac{3qrst}{2} $ to get $ \dfrac{ 3iqrst }{ 2 } $.

Step 1: Write $ i $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} i \cdot \frac{3qrst}{2} & \xlongequal{\text{Step 1}} \frac{i}{\color{red}{1}} \cdot \frac{3qrst}{2} \xlongequal{\text{Step 2}} \frac{ i \cdot 3qrst }{ 1 \cdot 2 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 3iqrst }{ 2 } \end{aligned} $$

Add $-1$ and $ \dfrac{3iqrst}{2} $ to get $ \dfrac{ \color{purple}{ 3iqrst-2 } }{ 2 }$.

Step 1: Write $ -1 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: To add raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the first fraction by $\color{blue}{ 2 }$.

$$ \begin{aligned} -1+ \frac{3iqrst}{2} & \xlongequal{\text{Step 1}} \frac{-1}{\color{red}{1}} + \frac{3iqrst}{2} = \frac{ \left( -1 \right) \cdot \color{blue}{ 2 }}{ 1 \cdot \color{blue}{ 2 }} + \frac{ 3iqrst }{ 2 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ -2 } }{ 2 } + \frac{ \color{purple}{ 3iqrst } }{ 2 }=\frac{ \color{purple}{ 3iqrst-2 } }{ 2 } \end{aligned} $$

Add $-2$ and $ \dfrac{3iqrst}{2} $ to get $ \dfrac{ \color{purple}{ 3iqrst-4 } }{ 2 }$.

Step 1: Write $ -2 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: To add raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the first fraction by $\color{blue}{ 2 }$.

$$ \begin{aligned} -2+ \frac{3iqrst}{2} & \xlongequal{\text{Step 1}} \frac{-2}{\color{red}{1}} + \frac{3iqrst}{2} = \frac{ \left( -2 \right) \cdot \color{blue}{ 2 }}{ 1 \cdot \color{blue}{ 2 }} + \frac{ 3iqrst }{ 2 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ -4 } }{ 2 } + \frac{ \color{purple}{ 3iqrst } }{ 2 }=\frac{ \color{purple}{ 3iqrst-4 } }{ 2 } \end{aligned} $$

Add $-1$ and $ \dfrac{3iqrst}{2} $ to get $ \dfrac{ \color{purple}{ 3iqrst-2 } }{ 2 }$.

Step 1: Write $ -1 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: To add raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the first fraction by $\color{blue}{ 2 }$.

$$ \begin{aligned} -1+ \frac{3iqrst}{2} & \xlongequal{\text{Step 1}} \frac{-1}{\color{red}{1}} + \frac{3iqrst}{2} = \frac{ \left( -1 \right) \cdot \color{blue}{ 2 }}{ 1 \cdot \color{blue}{ 2 }} + \frac{ 3iqrst }{ 2 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ -2 } }{ 2 } + \frac{ \color{purple}{ 3iqrst } }{ 2 }=\frac{ \color{purple}{ 3iqrst-2 } }{ 2 } \end{aligned} $$

Add $-1$ and $ \dfrac{3iqrst}{2} $ to get $ \dfrac{ \color{purple}{ 3iqrst-2 } }{ 2 }$.

Step 1: Write $ -1 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: To add raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the first fraction by $\color{blue}{ 2 }$.

$$ \begin{aligned} -1+ \frac{3iqrst}{2} & \xlongequal{\text{Step 1}} \frac{-1}{\color{red}{1}} + \frac{3iqrst}{2} = \frac{ \left( -1 \right) \cdot \color{blue}{ 2 }}{ 1 \cdot \color{blue}{ 2 }} + \frac{ 3iqrst }{ 2 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ -2 } }{ 2 } + \frac{ \color{purple}{ 3iqrst } }{ 2 }=\frac{ \color{purple}{ 3iqrst-2 } }{ 2 } \end{aligned} $$

Multiply $3iqrst$ by $ \dfrac{3iqrst-4}{2} $ to get $ \dfrac{ 9i^2q^2r^2s^2t^2-12iqrst }{ 2 } $.

Step 1: Write $ 3iqrst $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 3iqrst \cdot \frac{3iqrst-4}{2} & \xlongequal{\text{Step 1}} \frac{3iqrst}{\color{red}{1}} \cdot \frac{3iqrst-4}{2} \xlongequal{\text{Step 2}} \frac{ 3iqrst \cdot \left( 3iqrst-4 \right) }{ 1 \cdot 2 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 9i^2q^2r^2s^2t^2-12iqrst }{ 2 } \end{aligned} $$

Divide $ \dfrac{3iqrst-2}{2} $ by $ \dfrac{9i^2q^2r^2s^2t^2-12iqrst}{2} $ to get $ \dfrac{ 3iqrst-2 }{ 9i^2q^2r^2s^2t^2-12iqrst } $.

Step 1: To divide rational expressions, multiply the first fraction by the reciprocal of the second fraction.

Step 2: Cancel $ \color{red}{ 2 } $ in first and second fraction.

Step 3: Multiply numerators and denominators.

Step 4: Simplify numerator and denominator.

$$ \begin{aligned} \frac{ \frac{3iqrst-2}{2} }{ \frac{\color{blue}{9i^2q^2r^2s^2t^2-12iqrst}}{\color{blue}{2}} } & \xlongequal{\text{Step 1}} \frac{3iqrst-2}{2} \cdot \frac{\color{blue}{2}}{\color{blue}{9i^2q^2r^2s^2t^2-12iqrst}} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{3iqrst-2}{\color{red}{1}} \cdot \frac{\color{red}{1}}{9i^2q^2r^2s^2t^2-12iqrst} \xlongequal{\text{Step 3}} \frac{ \left( 3iqrst-2 \right) \cdot 1 }{ 1 \cdot \left( 9i^2q^2r^2s^2t^2-12iqrst \right) } = \\[1ex] & \xlongequal{\text{Step 4}} \frac{ 3iqrst-2 }{ 9i^2q^2r^2s^2t^2-12iqrst } \end{aligned} $$