Question

x^-2 - y^-2
_____________
x^-1 - y^-1

Answer 1

there is a slick way to do this, but it is more meaningful if you write what this really is without negative exponents

Answer 2

ok

Answer 3

\[\frac{\frac{1}{x^2}-\frac{1}{y^2}}{\frac{1}{x}-\frac{1}{y}}\]

Answer 4

ok then i find the lcd of the top and bottom

Answer 5

now multiply top and bottom by
\[x^2y^2\] to clear the fractions

Answer 6

lcd

Answer 7

ok

Answer 8

right. the slick way is to write
\[\frac{1}{x^2}-\frac{1}{y^2}=(\frac{1}{x}+\frac{1}{y})(\frac{1}{x}+\frac{1}{y})\] and then cancel

Answer 9

difference of squares

Answer 10

typo there should be
\[\frac{1}{x^2}-\frac{1}{y^2}=(\frac{1}{x}-\frac{1}{y})(\frac{1}{x}+\frac{1}{y})\]

Answer 11

cancels the bottom

Answer 12

yes if you do it that way and cancel, you get
\[\frac{1}{x}+\frac{1}{y}\] in one step

Answer 13

thats the answer?

Answer 14

yes unless you care to add them and get

\[\frac{x+y}{xy}\]

Answer 15

ok

Answer 16

thanks bro