Initial program 0.4
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
Simplified0.4
\[\leadsto \color{blue}{3 \cdot \left(\sqrt{x} \cdot \left(y + \left(\frac{1}{x \cdot 9} - 1\right)\right)\right)}\]
- Using strategy
rm Applied distribute-lft-in0.4
\[\leadsto 3 \cdot \color{blue}{\left(\sqrt{x} \cdot y + \sqrt{x} \cdot \left(\frac{1}{x \cdot 9} - 1\right)\right)}\]
Applied distribute-lft-in0.4
\[\leadsto \color{blue}{3 \cdot \left(\sqrt{x} \cdot y\right) + 3 \cdot \left(\sqrt{x} \cdot \left(\frac{1}{x \cdot 9} - 1\right)\right)}\]
- Using strategy
rm Applied sub-neg0.4
\[\leadsto 3 \cdot \left(\sqrt{x} \cdot y\right) + 3 \cdot \left(\sqrt{x} \cdot \color{blue}{\left(\frac{1}{x \cdot 9} + \left(-1\right)\right)}\right)\]
Applied distribute-lft-in0.4
\[\leadsto 3 \cdot \left(\sqrt{x} \cdot y\right) + 3 \cdot \color{blue}{\left(\sqrt{x} \cdot \frac{1}{x \cdot 9} + \sqrt{x} \cdot \left(-1\right)\right)}\]
Simplified0.4
\[\leadsto 3 \cdot \left(\sqrt{x} \cdot y\right) + 3 \cdot \left(\color{blue}{\frac{1}{9 \cdot \sqrt{x}}} + \sqrt{x} \cdot \left(-1\right)\right)\]
Simplified0.4
\[\leadsto 3 \cdot \left(\sqrt{x} \cdot y\right) + 3 \cdot \left(\frac{1}{9 \cdot \sqrt{x}} + \color{blue}{1 \cdot \left(-\sqrt{x}\right)}\right)\]
- Using strategy
rm Applied associate-/r*0.4
\[\leadsto 3 \cdot \left(\sqrt{x} \cdot y\right) + 3 \cdot \left(\color{blue}{\frac{\frac{1}{9}}{\sqrt{x}}} + 1 \cdot \left(-\sqrt{x}\right)\right)\]
- Using strategy
rm Applied pow10.4
\[\leadsto 3 \cdot \left(\sqrt{x} \cdot \color{blue}{{y}^{1}}\right) + 3 \cdot \left(\frac{\frac{1}{9}}{\sqrt{x}} + 1 \cdot \left(-\sqrt{x}\right)\right)\]
Applied pow10.4
\[\leadsto 3 \cdot \left(\color{blue}{{\left(\sqrt{x}\right)}^{1}} \cdot {y}^{1}\right) + 3 \cdot \left(\frac{\frac{1}{9}}{\sqrt{x}} + 1 \cdot \left(-\sqrt{x}\right)\right)\]
Applied pow-prod-down0.4
\[\leadsto 3 \cdot \color{blue}{{\left(\sqrt{x} \cdot y\right)}^{1}} + 3 \cdot \left(\frac{\frac{1}{9}}{\sqrt{x}} + 1 \cdot \left(-\sqrt{x}\right)\right)\]
Applied pow10.4
\[\leadsto \color{blue}{{3}^{1}} \cdot {\left(\sqrt{x} \cdot y\right)}^{1} + 3 \cdot \left(\frac{\frac{1}{9}}{\sqrt{x}} + 1 \cdot \left(-\sqrt{x}\right)\right)\]
Applied pow-prod-down0.4
\[\leadsto \color{blue}{{\left(3 \cdot \left(\sqrt{x} \cdot y\right)\right)}^{1}} + 3 \cdot \left(\frac{\frac{1}{9}}{\sqrt{x}} + 1 \cdot \left(-\sqrt{x}\right)\right)\]
Simplified0.4
\[\leadsto {\color{blue}{\left(\sqrt{x} \cdot \left(3 \cdot y\right)\right)}}^{1} + 3 \cdot \left(\frac{\frac{1}{9}}{\sqrt{x}} + 1 \cdot \left(-\sqrt{x}\right)\right)\]
Final simplification0.4
\[\leadsto \sqrt{x} \cdot \left(3 \cdot y\right) + 3 \cdot \left(\frac{\frac{1}{9}}{\sqrt{x}} + \sqrt{x} \cdot \left(-1\right)\right)\]
