Question

What is the simplified form of the quantity 1 over x minus 1 over y all over 1 over x plus 1 over y?

Answer 1

`\cfrac{ (1)/(x)- (1)/(y) }{ (1)/(x)+ (1)/(y) }= \cfrac{ (y-x)/(xy) }{ (y+x)/(xy) }= \cfrac{y-x}{y+x}`

Answer 2

Answer: Our simplified form will be

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

Explanation:

Since we have given that

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

We need to solve this to get a simplified form ;

So, we get,

`((1)/(x)-(1)/(y))/((1)/(x)+(1)/(y))\\\\\text{Taking L.C.M. of numerator and denominator separately}\\\\=((y-x)/(xy))/((x+y)/(xy))\\\\=(y-x)/(xy)* (xy)/(x+y)\\\\=(y-x)/(x+y)`

Hence, our simplified form will be

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