Help Please?

Question

1. Write answer in lowest term

5u/14t multiply 2tu/3

2. Write this as a single rational expression
4x^3/5ak^3 - 3a^2y/10c^3k

3. Subtract and simplify
5/x-1 - 3-2x/x

Thank you

Answer 1

1. When multiplying fractions, you just multiply across. That is, the numerator of your answer is the product of the numerators in the multiplicands, and the denominator in the answer is the product of the denominators.
Ex: a/b * c/d = ac/bd

Apply this to your problem:
5u/14t * 2tu/3 = 10tu^2/42t
Cancel out stuff: 10/42 can be reduced to 5/24, and you can cancel the t's (you have one t in the numerator and on in the denominator).
= 5u^2/24

2. What you need to do for this one is get a common denominator. Unlike multiplying and dividing, you can't just subtract across the fraction.
To get a common denominator, you need to choose a form of '1' by which to multiply each fraction. Since you're not allowed to change the value of the fraction, you have to multiply by 1. Anyway, the best way to get a common denominator is to multiply each fraction by the denominator of the other.
Ex: a/b - c/d
= a/b*(d/d) - c/d*(b/b)
= ad/bd - bc/bd = (ad - bc)/bd

Your equation is a tad more complicated than that, but I'm sure you can figure it out!

3. Again, get common denominators. I'm not sure if you mean 5/(x - 1) - (3 - 2x)/x. . . . You need to put some parentheses in your problem somewhere.
If your problem is how I've written it above, then your common denominator is simply the multiple of your two denominators: x(x - 1). Multiply each fraction by the appropriate expression for 1: that is, multiply the first fraction by x/x and multiply the second by (x-1)/(x-1).

Answer 2

Common, Chris...
(5u/14t)(2tu/3)... You know how to multiply fractions. Multiply the numerators (top numbers) to get the new numerator, and the denominators (bottom numbers) to get the new denominator.
Then, when you get the answer, factor the common terms out of the new numerator and denominator. 10=2*5, 42=2*21, and 2/2=1. Keep factoring out stuff until there's nothing left common in both numerator and denominator.

In the second, you need to get them over a common denominator. If you don't know how to find the lowest common denominator, just multiply the denominators together. That will give you a common denominator. But it means you'll have to do some work with the numerators to keep the fractions equal to their original value. For example 2/3+1/4 = 8/12 + 3/12 = 11/12... I had to multiply 2/3 by 4/4 to get 8/12, and 1/4 by 3/3 to get 3/12

Then you simply add 'em... or subtract one from the other. Once you get done with that, do that factoring thing again... just as you did in the first problem. But this time, whatever you factor out in the numerator has to be common to BOTH terms.

The third one is just like the second.

And, lest you want to take the posted answers, and not do your own work. Some of them are incorrect.

Answer 3

5u/14t * 2tu/3 =
10tu^2 / 42t =
2u^2 / 21


2. Write this as a single rational expression
4x^3/5ak^3 - 3a^2y/10c^3k =
Multiply to get the denominators the same (10ac^3k^3)
(4x^3(2c^3) - 3a^2y(ak^2)) / 10ac^3k^3 =
(8x^3c^3 - 3a^3k^2y) / 10ac^3k^3

3. Subtract and simplify
5/x-1 - 3-2x/x
I can't tell what the fractions are. Believe you are asking
5/(x-1) - (3-2x)/x =
5x/(x(x-1)) - (3-2x)(x-1)/(x(x-1)) =
(5x + (2x-3)(x-1)) / (x^2-x) =
(5x + 2x^2 -5x +3) / (x^2 - x) =
(2x^2 + 3) / (x^2-x)

Answer 4

5u/14t multiply 2tu/3
= 10tu^2/42t = 5u^2/21

2. Write this as a single rational expression
4x^3/5ak^3 - 3a^2y/10c^3k
= {[4x^3(2)ac^3] -[ 3a^2yk^2]}/ 10ac^3k^3
= [8x^3 ac^3 -3a^2yk^2]/10ac^3k^3
= 8x^3c^3 -3ayk^2)/10c^3k^3


3. Subtract and simplify
5/(x-1) - (3-2x)/x
[5x - (x-1)(3-2x)]/(x(x-1))
= [5x -5x +2x^2+3]/(x(x-1))
= (2x^2+3)/(x(x-1))