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 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!
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?
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 Quick
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??