Expressing answers and simple fractions: ((1/y-k)-(1/y)),...

[password]

Okay, I have two questions to ask about Here's the first one...

1) Express as a simple fraction: ( (1/y-k)-(1/y) ) / k

I got rid of the k denominator by multiplying it to the top ones, so now I have this...

1/yk-k^2 - 1/yk

But I have no clue what to do after this step. I'm unsure how to either get the other side to have a +k^2 so I could actually turn that into one fraction. Thanks

Here's my second question:

2) x(x-1)^(-1/2) + 2(x-1)^1/2

I understand that I can change (x-1)^(1/2) to the square root of (x-1)... But what would (x-1)^(-1/2) change to?

Thanks for you help

 

[morson]

For the first one, one must recognise that the simplifications only hold if k and y aren't 0, nor is k equal to y.

I'd multiply your fraction you have by y(y - k)/y(y - k), so you get:

(y - (y - k))/ky(y - k)

So, simplify it a bit and you get:

1/[y(y - k)]

Also, (x - 1)^(-1/2) = 1/sqrt(x-1)

 

[stapel]

Here's my second question:

2) x(x-1)^(-1/2) + 2(x-1)^1/2

Are the instructions the same, "Express as a simple fraction", for this exercise? If so, use the hint provided earlier:

. . . . .(x - 1)^-1 = 1 / sqrt[x - 1]

Create a common denominator (by multiplying the second fraction by the appropriate square root), and then combine the two expressions.

If not, please reply with the instructions, showing what you have tried so far. Thank you!

Eliz.