Please explain the breakdown of simplifying: -(2\sqrt(7))/(15\sqrt(2)) to getting: -(\sqrt(14))/(15).?

2 / √7

--------

15 / √2

2 √2

-------

15 √7

2 √14

-------

105

Is that:

(-2 / √7) / (15 / √2) to get to -√14 / 15

Let's see if that's what I get. The first thing I'll do is to turn the division of fractions into the multiplication of the reciprocal:

(-2 / √7) / (15 / √2)

(-2 / √7) * (√2 / 15)

Next, I'll rationalize the first fraction by multiplying both halves by √7:

(-2√7 / 7) * (√2 / 15)

then now we don't get what you are expecting.

So guessing again:

-2√7 / (15√2)

This looks like it will do what we want. Rationalize the denominator by multiplying both halves by √2:

-2√14 / (15 * 2)

Now the 2's can cancel out:

-√14 / 15

And that's what you are looking to get.

So I hope this answers your question. The \ you used in your sqrt was confusing and should be avoided in the future. If you would have just done:

-(2 sqrt(7)) / (15 sqrt(2))

that would have made more sense.