simplify expressions (1/y-x)+(x/(x-y)^2), ((x+y)/(x-y))^2-1

evryothrsnisused

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i need help on a couple of problems...

the first one is (1/y-x)+(x/(x-y)^2)

the second one is ((x+y)/(x-y))^2-1
 
evryothrsnisused said:
i need help on a couple of problems...

the first one is (1/y-x)+(x/(x-y)^2)

the second one is ((x+y)/(x-y))^2-1

Does your problem look like:

\(\displaystyle \frac{1}{y} \, - \, x \, + \, \frac{x}{(x \, - \, y)^2}\)

That is what you wrote.

If you meant to write:

\(\displaystyle \frac{1}{y \, - \, x} \, + \, \frac{x}{(x \, - \, y)^2}\)

then you should have written:

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

Assuming it is the second form following are some hints

Re-write (x-y)^2 as (y-x)^2 -- because those are equal.

Then treat those as if you are doing a numerical fraction addition.

So the next step would be - what is the Lowest-common-multiple (LCM some times called LCD) of the denominators.

Multiply and divide by appropriate expressions - so that the denominators are equal (just like you would do to find 1/2 + 1/3 without a calculator).

Then do the addition and simplify.

If you are still stuck write back showing your work and tell us exactly where you are stuck.
 
thanks for the help on that one...

i still need some help getting started on the second one though...

it is ((x+y)/(x-y))^2-1
 
Hello, evryothrsnisused!

\(\displaystyle \left(\frac{x+y}{x-y}\right)^2-1\)

\(\displaystyle \text{We have: }\;\frac{(x+y)^2}{(x-y)^2} - 1\)

. . . . . \(\displaystyle =\;\;\frac{(x+y)^2}{(x-y)^2} - \frac{(x-y)^2}{(x-y)^2}\)

. . . . . \(\displaystyle = \;\;\frac{(x^2 + 2xy + y^2) - (x^2 - 2xy + y^2)}{(x-y)^2}\)

. . . . . \(\displaystyle =\;\;\frac{x^2 + 2xy + y^2 - x^2 + 2xy - y^2}{(x-y)^2}\)

. . . . . \(\displaystyle =\;\;\frac{4xy}{(x-y)^2}\)

 
evryothrsnisused said:
... need some help getting started on the second one ...

Hi evryothrsnisused:

\(\displaystyle (\frac{x+y}{x-y})^2\;-\;1\)

This expression can be factored as a difference-of-squares.

\(\displaystyle (\frac{x+y}{x-y}+1)(\frac{x+y}{x-y}-1)\)

Try simplifying the expression in each set of parentheses; then multiply them.

Let us know if you need more help getting finished. (I'm off to figure out how to get "big" parentheses in LaTeX.)

Cheers,

~ Mark :)

Edits: corrected some spelling errors
 
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