Question

What is 1/x - 1/y over 1/x^2 - 1/ y^2 equal to?

Answer 1

multiply top and bottom by
\[x^2y^2\] to get the answer in the fewest steps

Answer 2

or factor the denominator as the difference of two squares and cancel with the numerator.

Answer 3

depending on how fancy you want to be

Answer 4

or note that 1/x^2 - 1/y^2 = (1/x+1/y)(1/x-1/y)

Answer 5

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

Answer 6

now multiply top and bottom by
\[xy\] to get
\[\frac{xy}{y+x}\]

Answer 7

Thank you