Question

How do you simplify `(x/y - y/x)/(1/y + 1/x)` and can you use a calculator to simplify?

Answer 1

`color(red)"The answer is (x-y)"`

Explanation:

`{(x/y)-(y/x)}/{(1/x)-(1/y)}`

On further solving this problem we get,

`{(x^2-y^2)/(xy)}/{(x+y)/(xy)}`

Now dividing both the sides we get, `xy` as cancelled from both the numerator and denominator.

`{(x+y)(x-y)}/(x+y)`

Cancelling `x+y` from both numerator and denominator we get,

Ans. = `(x-y)`

Answer 2

Looking at the numerator

`x/y-y/x` if we put them over a common denominator

`(x^2-y^2)/(xy)`

Now looking at the denominator

`1/y+1/x` and put this over a common denominator

`(x+y)/(xy)`

So we have

`[(x^2-y^2)/(xy)]/[(x+y)/(xy)]`

`(x^2-y^2)/(xy)xx(xy)/(x+y)`

`(x^2-y^2)/(x+y)`

`[(x+y)(x-y)]/(x+y)`

`x-y`