\(\frac{1}{{\left(\frac{f}{-\left(n + f\right)}\right)}^3 - {\left(\frac{n}{-\left(n + f\right)}\right)}^3} \cdot \left({\left(\frac{f}{-\left(f + n\right)}\right)}^2 + \left({\left(\frac{n}{-\left(f + n\right)}\right)}^2 + \frac{f}{-\left(f + n\right)} \cdot \frac{n}{-\left(f + n\right)}\right)\right)\)
- Started with
\[\frac{-\left(f + n\right)}{f - n}\]
0.1
- Using strategy
rm 0.1
- Applied clear-num to get
\[\color{red}{\frac{-\left(f + n\right)}{f - n}} \leadsto \color{blue}{\frac{1}{\frac{f - n}{-\left(f + n\right)}}}\]
0.1
- Using strategy
rm 0.1
- Applied div-sub to get
\[\frac{1}{\color{red}{\frac{f - n}{-\left(f + n\right)}}} \leadsto \frac{1}{\color{blue}{\frac{f}{-\left(f + n\right)} - \frac{n}{-\left(f + n\right)}}}\]
0.1
- Using strategy
rm 0.1
- Applied flip3-- to get
\[\frac{1}{\color{red}{\frac{f}{-\left(f + n\right)} - \frac{n}{-\left(f + n\right)}}} \leadsto \frac{1}{\color{blue}{\frac{{\left(\frac{f}{-\left(f + n\right)}\right)}^{3} - {\left(\frac{n}{-\left(f + n\right)}\right)}^{3}}{{\left(\frac{f}{-\left(f + n\right)}\right)}^2 + \left({\left(\frac{n}{-\left(f + n\right)}\right)}^2 + \frac{f}{-\left(f + n\right)} \cdot \frac{n}{-\left(f + n\right)}\right)}}}\]
0.1
- Applied associate-/r/ to get
\[\color{red}{\frac{1}{\frac{{\left(\frac{f}{-\left(f + n\right)}\right)}^{3} - {\left(\frac{n}{-\left(f + n\right)}\right)}^{3}}{{\left(\frac{f}{-\left(f + n\right)}\right)}^2 + \left({\left(\frac{n}{-\left(f + n\right)}\right)}^2 + \frac{f}{-\left(f + n\right)} \cdot \frac{n}{-\left(f + n\right)}\right)}}} \leadsto \color{blue}{\frac{1}{{\left(\frac{f}{-\left(f + n\right)}\right)}^{3} - {\left(\frac{n}{-\left(f + n\right)}\right)}^{3}} \cdot \left({\left(\frac{f}{-\left(f + n\right)}\right)}^2 + \left({\left(\frac{n}{-\left(f + n\right)}\right)}^2 + \frac{f}{-\left(f + n\right)} \cdot \frac{n}{-\left(f + n\right)}\right)\right)}\]
0.1
- Applied simplify to get
\[\color{red}{\frac{1}{{\left(\frac{f}{-\left(f + n\right)}\right)}^{3} - {\left(\frac{n}{-\left(f + n\right)}\right)}^{3}}} \cdot \left({\left(\frac{f}{-\left(f + n\right)}\right)}^2 + \left({\left(\frac{n}{-\left(f + n\right)}\right)}^2 + \frac{f}{-\left(f + n\right)} \cdot \frac{n}{-\left(f + n\right)}\right)\right) \leadsto \color{blue}{\frac{1}{{\left(\frac{f}{-\left(n + f\right)}\right)}^3 - {\left(\frac{n}{-\left(n + f\right)}\right)}^3}} \cdot \left({\left(\frac{f}{-\left(f + n\right)}\right)}^2 + \left({\left(\frac{n}{-\left(f + n\right)}\right)}^2 + \frac{f}{-\left(f + n\right)} \cdot \frac{n}{-\left(f + n\right)}\right)\right)\]
0.1
