what is 1/x+1/y = ? is it equal to 1/x+y or what?

Hi,

Try it with some numbers. Suppose that x = y = 2 then your question is

What is 1/2 + 1/2? Is it 1/(2+2) = 1/4? Certainly not! 1/2 + 1/2 = 1 not 1/4.

Suppose you are making making pancakes, the recipe calls for 1/2 a litre of milk and makes 12 pancakes. You need 18 pancakes and hence you need one and a half recipes. Half of 1/2 is 1/4 so you need 1/2 plus 1/4 liters of milk.

What is 1/2 + 1/4? Is it 1/(2+4) = 1/6? Certainly not! 1/6 is less than 1/2!
1/2 + 1/4 = 3/4 not 1/6.

To add fractions you need a common denominator.

1/2 + 1/4 = 2/4 + 1/4 = (2+1)/4 = 3/4

With 1/x + 1/y you also need a common denominator. A common denominator for 1/x and 1/y is xy.

1/x = y/(xy) and 1/y = x/(xy)

thus

1/x + 1/y = y/xy + x/xy = (y + x)/xy

I hope this helps,
Penny