Verify simplification please

**jay1** · January 21st 2010, 07:04 PM

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!

**VonNemo19** · January 21st 2010, 07:23 PM

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

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

**jay1** · January 21st 2010, 07:29 PM

Originally Posted by VonNemo19

Do you mean

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

Yes! I'm sorry if it was ambiguous

**VonNemo19** · January 21st 2010, 07:35 PM

Originally Posted by jay1

Yes! I'm sorry if it was ambiguous

Then we would multiply Den. and Num. by $q^2r^2$ giving $\frac{r^2-q^2}{r^2q-q^2r}=\frac{(r+q)(r-q)}{qr(r-q)}=\frac{r+q}{qr}$

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