Math Is Fun Forum

MidnightMoon

Guest

How Do You Simplify These Expressions?

I'm really stuck on these 3 questions. I can't figure out how the book got their answers. Can anyone help me? Or at least guide me through one of them?

1.

2.

3.

Furthermore there is this question which I'm not sure how to go around...

If

,

and

, show that xyz=1.

Thank you in advance.

MidnightMoon

Guest

Re: How Do You Simplify These Expressions?

Okay, I have worked out the 1st and 4th questions. But I'm still having difficulties with the 3rd and 4th. >_<

MidnightMoon

Guest

Re: How Do You Simplify These Expressions?

I meant 2nd and 3rd question previously. But after much more confusion... and mistakes. For the 3rd question, I have gotten as far as this:

{[a√(ab)][√a+√b]} all divided by (a-b). But how do you multiply the numerator out?

I have yet the 2nd one to tackle. >_<

MidnightMoon

Guest

Re: How Do You Simplify These Expressions?

Okay, I've just done the 3rd one. Only the 2nd one left. >_< I have no idea how to change the denominator into a^2+b... Any suggestiosn or ideas? I have this equation now:

(b^(5/2))*(a^(3/2))+ab all divided by ((a^2)*(b^1/2))+(b^3/2)

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: How Do You Simplify These Expressions?

I would recommend not writing:

But instead:

This makes where you need to simplify much more visible.  Now for simplifying any of these, the typical steps are get a single fraction in the denominator by combining the fractions, then "flipping" it up.  In general:

So if you have:

Then that equals:

And then "flip" it up:

---

"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."