Help with more fractions

[alaska33355]

Here is the problem:

2/x + 1/2x

It does not look hard, but we are stumped. We cannot combine the x and the 2x, because the desired answer is
5/2x. Can someone help me with the next step?

Thanks a million! (to the 5th power)

 

[alohacharlie]

We can not add fractions unless they have a common denominator.

Your denominators are x and 2x

We can make the x into 2x by multiplying by 2

(2) 2
(2) x gives us 4/2x

Note that we multiplied the numerator (top number) by 2 also. You can change the appearance of the fraction 2/x but the value has to remain the same.

To do that we must multiply the top by the same amount that we do the bottom.

Why does this work?? We multiplied 2/x by 2/2. What is 2/2? It's another way of writing 1. And if you multiply anything by 1, the value stays the same.

So we changed the appearance (now it has 2x for a denominator) but it has the same value it always had.

So now you have

4 + 1
2x 2x

which adds up to the answer you had.
Hope it helps.

 

[alaska33355]

Thanks, Aloha Charlie! It makes sense......wonder why I couldn't see it?