Question 167820
x to the -1 plus y to the -1 divided by x squared minus y squared.
.
{{{ (x^-1 + y^-1)/(x^2-y^2)}}}
.
{{{ (1/x + 1/y)/(x^2-y^2)}}}
.
Multiplying numerator and denominator by xy:
{{{ (1/x + 1/y)(xy)/(x^2-y^2)(xy)}}}
{{{ (1/x + 1/y)(xy)/(x^2-y^2)(xy)}}}
{{{ (y + x)/(x^2-y^2)(xy)}}}
Factoring the denominator:
{{{ (y + x)/(x+y)(x-y)(xy)}}}
Canceling like-terms:
{{{ 1/(x-y)(xy)}}}
Or,
{{{ 1/(x^2y-xy^2)}}}