Just want to ensure that I have simplified/solved the following expressions correctly 1) (q^-2) - (r^-2) / (q^-1) - (r^-1) I have (-r -q)/(qr)? 2) 1/2 + 7/y = 2 + 1/y I have y=3? Thanks!

2. Originally Posted by jay1
Just want to ensure that I have simplified/solved the following expressions correctly 1) (q^-2) - (r^-2) / (q^-1) - (r^-1) I have (-r -q)/(qr)? 2) 1/2 + 7/y = 2 + 1/y I have y=3? Thanks!
Do you mean

$\frac{q^{-2}-r^{-2}}{q^{-1}-r^{-1}}$ ?

3. Originally Posted by VonNemo19
Do you mean

$\frac{q^{-2}-r^{-2}}{q^{-1}-r^{-1}}$ ?
Yes! I'm sorry if it was ambiguous

4. Originally Posted by jay1
Yes! I'm sorry if it was ambiguous
Then we would multiply Den. and Num. by $q^2r^2$ giving $\frac{r^2-q^2}{r^2q-q^2r}=\frac{(r+q)(r-q)}{qr(r-q)}=\frac{r+q}{qr}$