Question

(q^(-2)-r^(-2))/(q^(-1)-r^(-1))

Answer 1

First recognize that \[q^{-2}-r^{-2}=\left( q^{-1} \right)^2-\left( r^{-1} \right)^2\] and then apply the difference of two squares,\[\left( {q^{-1}} \right)^2-\left( {r^{-1}} \right)^2=\left( q^{-1}-r^{-1} \right)\left( q^{-1}+r^{-1} \right)\]so your original question takes the form\[\frac{\left( q^{-1}-r^{-1} \right)\left(q^{-1}+r^{-1} \right)}{q^{-1}-r^{-1}}=q^{-1}+r^{-1}\]