Simplifying Fractions - Am I right?

Instruction: Write a single fraction with one numerator and one denominator.

Problem#1:

1/x + 1/y

I think the answer should be x+y/xy, yes?

Problem #2:

(5a^-1 + 2b^-1) / (3a^-2 - 2b^-2)

I think the answer should be (3a-b) / 5, yes?

Problem #3:

[9-(1/y^2)] / [9+ (6/y) + (1/y^2)]

I think the answer should be 1 / (6/y), yes?

Problem #4 says to factor completely:

18y^3 + 48y^2 + 42y

I think the final answer should be 6y(3y^2 + 8y + 7), yes?

Thank you!

Simplifying Fraction - Am I Right? Part 2

You guys are great for helping.

Let me see if I'm getting the hang of it now.

Is this right?

[(x+1)/x] / [(x-3)/4]

To get rid of the fractions, I'll multiply the denominator and numerator by 4x.

The result is 4x + 4 / x^2 - 3x, which can be reduced to

4(x+1)/x(x-3)

Am I right this time?

Simplify Fractions - Am I Right? Part 3

I'm on a roll. I am fairly certain I have the first 2 problems correct, but the last 2 are trickier.

1. [5-(1/a)] / (a+b)

Final answer is (5a-1) / [a(a+b)]

2. [(2x +1) / (x^2 - 25)] / [(4x^2 -1) / (x-5)]

Final answer is (2x + 1) / [(4x^2 -1)(x+5)]

3. {[1/(x+h)] - (1/x)} / h

For this one, I multiplied the denominator & numerator by x(x+h) and eventually ended with a final answer of [x-(x+h)] / [xh(x + h)], which I don't think can be further simplified.

4. (x-y) / [(the square root of x) + (the square root of y)]

I don't think this can be simplified any further. (?)

Thank you for helping me - I am learning a lot.

Simplifying Fractions - Part 3

Quote:

Originally Posted by **Quick**

There is a rule in math that says "A fraction is not completely simplified until you rationalize the denominator"

OK... so let me give this a try.

The original problem is: (x-y) / (square root of x) + (square root of y)

If I rationalize the denominator, I'd be multiplying it and the numerator by the (square root of x) + (square root of y)......right?

So, I end up with:

(x-y)[(square root of x) + (square root of y)] / (x+y)

And this can't be simplified further.

Am I right??