## anonymous 5 years ago (x^(-2)-y^(-2))/(x^(-1)-y^(-1)) please?

1. anonymous

${x^{-2}-y^{-2} \over x^{-1}-y^{-1}}?$

2. amistre64

$\frac{x^{-2}-y^{-2}}{x^{-1}-y^{-1}}$ right?

3. amistre64

its just a matter of flipping all the ^- exponents to their reciprocals and re writeing it

4. amistre64

what part are you stuck at?

5. anonymous

$x ^{-1}-y ^{-1}$

6. anonymous

Just factor the numerator: $={(x^{-1}-y^{-1})(x^{-1}+y^{-1}) \over x^{-1}-y^{-1}}=x^{-1}+y^{-1}$

7. anonymous

so is it 1/x-y

8. anonymous

$\frac{x^{-2}-y^{-2}}{x^{-1}-y^{-1}}=\frac{\frac{1}{x^2}-\frac{1}{y^2}}{\frac{1}{x}-\frac{1}{y}}$ Answar's ways method is the correct snappy way to do it but if you want to see why it is true, multiply numerator and denominator by $x^2y^2$ to clear the fractions, or subtract and divide and you will get $\frac{y-x}{xy}$

9. anonymous

wow, thanks satelite73! how do i give a medal for your answer? you had the clearest solution of all! made me really understand the problem well. :) THANK YOU SO MUCH TO THE OTHERS AS WELL! <3

10. anonymous

By the way satellite, it's Anwar :) .. My way is simpler if you focus :P

11. anonymous

you're right Anwar! it is! i guess i just have to be more focused!