Question 125
We know it is $A=\frac{a^{-2}-b^{-2}}{a^{-1}-b^{-1}}$
$$
\text{and}\quad B=\left(\frac{a^{-1}}{a^{-1}-b^{-1}}-\frac{b^{-1}}{a^{-1}+b^{-1}}\right) \cdot\left(a^{-1}-b^{-1}\right) \cdot\left(a^{-2}+b^{-2}\right)^{-1}
$$
Prove that $A=B^{-1}$.
$$
\text{and}\quad B=\left(\frac{a^{-1}}{a^{-1}-b^{-1}}-\frac{b^{-1}}{a^{-1}+b^{-1}}\right) \cdot\left(a^{-1}-b^{-1}\right) \cdot\left(a^{-2}+b^{-2}\right)^{-1}
$$
Prove that $A=B^{-1}$.