$$2sqrt\dfrac{x-1}{s}qrt(x+1)\dfrac{x+1}{2}=\dfrac{2q^2r^2st^2x^3+2q^2r^2st^2x^2-2q^2r^2st^2x-2q^2r^2st^2}{2s}$$
Tap the blue circles to see an explanation.
| $$ \begin{aligned}2sqrt\frac{x-1}{s}qrt(x+1)\frac{x+1}{2}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}2 \cdot \frac{qrstx-qrst}{s}qrt(x+1)\frac{x+1}{2} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}2 \cdot \frac{q^2rstx-q^2rst}{s}rt(x+1)\frac{x+1}{2} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}2 \cdot \frac{q^2r^2stx-q^2r^2st}{s}t(x+1)\frac{x+1}{2} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}2 \cdot \frac{q^2r^2st^2x-q^2r^2st^2}{s}(x+1)\frac{x+1}{2} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}2 \cdot \frac{q^2r^2st^2x^2-q^2r^2st^2}{s}\frac{x+1}{2} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}\frac{2q^2r^2st^2x^2-2q^2r^2st^2}{s}\frac{x+1}{2} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle7}{\textcircled {7}} } }}}\frac{2q^2r^2st^2x^3+2q^2r^2st^2x^2-2q^2r^2st^2x-2q^2r^2st^2}{2s}\end{aligned} $$ | |
| ① | Multiply $qrst$ by $ \dfrac{x-1}{s} $ to get $ \dfrac{ qrstx-qrst }{ s } $. 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. $$ \begin{aligned} qrst \cdot \frac{x-1}{s} & \xlongequal{\text{Step 1}} \frac{qrst}{\color{red}{1}} \cdot \frac{x-1}{s} \xlongequal{\text{Step 2}} \frac{ qrst \cdot \left( x-1 \right) }{ 1 \cdot s } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ qrstx-qrst }{ s } \end{aligned} $$ |
| ② | Multiply $ \dfrac{qrstx-qrst}{s} $ by $ q $ to get $ \dfrac{ q^2rstx-q^2rst }{ 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. $$ \begin{aligned} \frac{qrstx-qrst}{s} \cdot q & \xlongequal{\text{Step 1}} \frac{qrstx-qrst}{s} \cdot \frac{q}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ \left( qrstx-qrst \right) \cdot q }{ s \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ q^2rstx-q^2rst }{ s } \end{aligned} $$ |
| ③ | Multiply $ \dfrac{q^2rstx-q^2rst}{s} $ by $ r $ to get $ \dfrac{ q^2r^2stx-q^2r^2st }{ 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. $$ \begin{aligned} \frac{q^2rstx-q^2rst}{s} \cdot r & \xlongequal{\text{Step 1}} \frac{q^2rstx-q^2rst}{s} \cdot \frac{r}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ \left( q^2rstx-q^2rst \right) \cdot r }{ s \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ q^2r^2stx-q^2r^2st }{ s } \end{aligned} $$ |
| ④ | Multiply $ \dfrac{q^2r^2stx-q^2r^2st}{s} $ by $ t $ to get $ \dfrac{ q^2r^2st^2x-q^2r^2st^2 }{ 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. $$ \begin{aligned} \frac{q^2r^2stx-q^2r^2st}{s} \cdot t & \xlongequal{\text{Step 1}} \frac{q^2r^2stx-q^2r^2st}{s} \cdot \frac{t}{\color{red}{1}} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \left( q^2r^2stx-q^2r^2st \right) \cdot t }{ s \cdot 1 } \xlongequal{\text{Step 3}} \frac{ q^2r^2st^2x-q^2r^2st^2 }{ s } \end{aligned} $$ |
| ⑤ | Multiply $ \dfrac{q^2r^2st^2x-q^2r^2st^2}{s} $ by $ x+1 $ to get $ \dfrac{q^2r^2st^2x^2-q^2r^2st^2}{s} $. Step 1: Write $ x+1 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{q^2r^2st^2x-q^2r^2st^2}{s} \cdot x+1 & \xlongequal{\text{Step 1}} \frac{q^2r^2st^2x-q^2r^2st^2}{s} \cdot \frac{x+1}{\color{red}{1}} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \left( q^2r^2st^2x-q^2r^2st^2 \right) \cdot \left( x+1 \right) }{ s \cdot 1 } \xlongequal{\text{Step 3}} \frac{ q^2r^2st^2x^2+ \cancel{q^2r^2st^2x} -\cancel{q^2r^2st^2x}-q^2r^2st^2 }{ s } = \\[1ex] &= \frac{q^2r^2st^2x^2-q^2r^2st^2}{s} \end{aligned} $$ |
| ⑥ | Multiply $2$ by $ \dfrac{q^2r^2st^2x^2-q^2r^2st^2}{s} $ to get $ \dfrac{ 2q^2r^2st^2x^2-2q^2r^2st^2 }{ s } $. Step 1: Write $ 2 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 2 \cdot \frac{q^2r^2st^2x^2-q^2r^2st^2}{s} & \xlongequal{\text{Step 1}} \frac{2}{\color{red}{1}} \cdot \frac{q^2r^2st^2x^2-q^2r^2st^2}{s} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ 2 \cdot \left( q^2r^2st^2x^2-q^2r^2st^2 \right) }{ 1 \cdot s } \xlongequal{\text{Step 3}} \frac{ 2q^2r^2st^2x^2-2q^2r^2st^2 }{ s } \end{aligned} $$ |
| ⑦ | Multiply $ \dfrac{2q^2r^2st^2x^2-2q^2r^2st^2}{s} $ by $ \dfrac{x+1}{2} $ to get $ \dfrac{ 2q^2r^2st^2x^3+2q^2r^2st^2x^2-2q^2r^2st^2x-2q^2r^2st^2 }{ 2s } $. Step 1: Multiply numerators and denominators. Step 2: Simplify numerator and denominator. $$ \begin{aligned} \frac{2q^2r^2st^2x^2-2q^2r^2st^2}{s} \cdot \frac{x+1}{2} & \xlongequal{\text{Step 1}} \frac{ \left( 2q^2r^2st^2x^2-2q^2r^2st^2 \right) \cdot \left( x+1 \right) }{ s \cdot 2 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ 2q^2r^2st^2x^3+2q^2r^2st^2x^2-2q^2r^2st^2x-2q^2r^2st^2 }{ 2s } \end{aligned} $$ |