Thread: 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!

Originally Posted by tesla1410

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

Problem#1:

1/x + 1/y
I think the answer should be 1/x+y, yes?

Originally Posted by tesla1410

Instruction: Write a single fraction with one numerator and one denominator.
(5a^-1 + 2b^-1) / (3a^-2 - 2b^-2)
I think the answer should be (3a-b) / 5, yes?

.

I didn't look at 3, since it's the same method as above, but 1 and 4 look good now.

-Dan

Originally Posted by tesla1410

Problem #4 says to factor completely:
18y^3 + 48y^2 + 42y
I think the final answer should be 6y(3y^2 + 8y + 7), yes?

this looks good
i dont have time now for the others ...maybe some one else can help
dan

Originally Posted by tesla1410

Problem #3:
[9-(1/y^2)] / [9+ (6/y) + (1/y^2)]
I think the answer should be 1 / (6/y), yes?

Multiply demoninator and numerator by ,

Thus,

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?

Originally Posted by tesla1410

Am I right this time?

Yes

Originally Posted by tesla1410

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?

nice work...i think you got it

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.

Originally Posted by tesla1410

4.

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

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

Originally Posted by tesla1410

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.

The first two did not dim my eye. Perhaps they are correct.
This one did.
It can be simplified.

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

It can.


Difference of two squares.

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??

Originally Posted by tesla1410

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??

Hacker solved this, but I would like to pount out that your calculations are wrong anyway...

Originally Posted by tesla1410

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??

If you choose to ignore my method and use rationalization instead:

The denominator is,

Thus,