Multiply $ \dfrac{1}{s} $ by $ q $ to get $ \dfrac{ q }{ s } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{1}{s} \cdot q & \xlongequal{\text{Step 1}} \frac{1}{s} \cdot \frac{q}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 1 \cdot q }{ s \cdot 1 } \xlongequal{\text{Step 3}} \frac{ q }{ s } \end{aligned} $$

Find $ \left(qrstx+1\right)^2 $ using formula.

$$ (A + B)^2 = \color{blue}{A^2} + 2 \cdot A \cdot B + \color{red}{B^2} $$

where $ A = \color{blue}{ qrstx } $ and $ B = \color{red}{ 1 }$.

$$ \begin{aligned}\left(qrstx+1\right)^2 = \color{blue}{\left( qrstx \right)^2} +2 \cdot qrstx \cdot 1 + \color{red}{1^2} = q^2r^2s^2t^2x^2+2qrstx+1\end{aligned} $$

Multiply $ \dfrac{q}{s} $ by $ r $ to get $ \dfrac{ qr }{ s } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{q}{s} \cdot r & \xlongequal{\text{Step 1}} \frac{q}{s} \cdot \frac{r}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ q \cdot r }{ s \cdot 1 } \xlongequal{\text{Step 3}} \frac{ qr }{ s } \end{aligned} $$

Find $ \left(qrstx+1\right)^2 $ using formula.

$$ (A + B)^2 = \color{blue}{A^2} + 2 \cdot A \cdot B + \color{red}{B^2} $$

where $ A = \color{blue}{ qrstx } $ and $ B = \color{red}{ 1 }$.

$$ \begin{aligned}\left(qrstx+1\right)^2 = \color{blue}{\left( qrstx \right)^2} +2 \cdot qrstx \cdot 1 + \color{red}{1^2} = q^2r^2s^2t^2x^2+2qrstx+1\end{aligned} $$

Multiply $ \dfrac{qr}{s} $ by $ t $ to get $ \dfrac{ qrt }{ s } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

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

Find $ \left(qrstx+1\right)^2 $ using formula.

$$ (A + B)^2 = \color{blue}{A^2} + 2 \cdot A \cdot B + \color{red}{B^2} $$

where $ A = \color{blue}{ qrstx } $ and $ B = \color{red}{ 1 }$.

$$ \begin{aligned}\left(qrstx+1\right)^2 = \color{blue}{\left( qrstx \right)^2} +2 \cdot qrstx \cdot 1 + \color{red}{1^2} = q^2r^2s^2t^2x^2+2qrstx+1\end{aligned} $$

Multiply $ \dfrac{qrt}{s} $ by $ \dfrac{x}{q^2r^2s^2t^2x^2+2qrstx+1} $ to get $ \dfrac{ qrtx }{ q^2r^2s^3t^2x^2+2qrs^2tx+s } $.

Step 1: Multiply numerators and denominators.

Step 2: Simplify numerator and denominator.

$$ \begin{aligned} \frac{qrt}{s} \cdot \frac{x}{q^2r^2s^2t^2x^2+2qrstx+1} & \xlongequal{\text{Step 1}} \frac{ qrt \cdot x }{ s \cdot \left( q^2r^2s^2t^2x^2+2qrstx+1 \right) } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ qrtx }{ q^2r^2s^3t^2x^2+2qrs^2tx+s } \end{aligned} $$