Question

Question 73

Show that x^-1 - y^-1/ x-y = -1/xy
where x is not equal to 0, y is not equal to 0 and y is not equal to x

Answer 1

see explanation

Explanation:

using the rule of exponents

`a^(-1)` =
`(1)/(a)`

`(x^(-1)-y^(-1) )/(x-y)`

=
`((1)/(x)-(1)/(y) )/(x-y)`

=
`((y-x)/(xy) )/(x-y)`

=
`(-(x-y))/(xy)` ×
`(1)/(x-y)` ← cancel (x - y) on numerator and denominator

= -
`(1)/(xy)`