Question

Subtract 5/(x^2-xy) - 5/(y^2-xy). Could somebody explain to me how to do this?

Answer 1

You must have the same denominators so :\[= [5(y-x) - 5(x-y)]/x(x-y)(y-x)\]\[= (5y-5x-5x+5y)/x(x-y)(y-x) \]\[= (10y-10x)/x(x-y)(y-x)\]\[= 10(y-x)/x(x-y)(y-x)\]\[= 10/x(x-y)\]

^_^

Answer 2

what I really need is how to find the LCD? I'm kind of confused

Answer 3

first factor, then you have to multiply both sides to get the same denominator

Answer 4

isn't the denominator xy(x-y)(x-y)?

Answer 5

or am i wrong?

Answer 6

if you notice , when you factor the denominator on the first side you'll get :

x(x-y)

and when you factor the denominator of the other side you get :
x(y-x)

we have x in common, but one has (x-y) and the other has (y-x) so we multiply the first one with (y-x) and the second one with (x-y) so both can have :

x(x-y)(y-x) the same denominator ^_^

clearer now? :)

Answer 7

no laka, youre right...

Answer 8

no laka, it's not ^_^ you'll get x^3

Answer 9

starica, the second denominator, factored, gives you y(y-x) not x(y-x)

Answer 10

yeah i realised

Answer 11

you sure?

Answer 12

oh right! ^^" sorry for the mess again

Answer 13

xy(y-x)(x-y)?

Answer 14

so you'll have to multiply x and y with the others too

Answer 15

yes laka, you are right dear, thank you ^_^

Answer 16

answer should be something like 5(xx-yy)/xy(x-y)(y-x)
or 5(xx-yy)/-xy(x-y)^2 aka -5(xx-yy)/(xy(x-y)^2

Answer 17

I'll have to redo it again ._.

Answer 18

im curious starica, how are you on here like all day? O.o

Answer 19

lol I wasn't here all day ^_^ I come in mornings and nights only

Answer 20

outcast girl the answer is :\[= 5y(y-x) - 5x(x-y)/xy(y-x)(x-y)\]\[= 5y^2 -5xy -5x^2 +5xy/xy(x-y)(y-x)\]\[= 5(y^2-x^2)/xy(x-y)(y-x)\]\[= 5(y-x)(y+x)/xy(x-y)(y-x)\]\[= 5(y+x)/xy(x-y)\]

for the mess up, I'm sure this time ^_^

Answer 21

sorry for the mess*

Answer 22

that's correct :)

Answer 23

how do you get the pretty notation?

Answer 24

yay , lol ^_^

Answer 25

click on equation and write it down ^_^

Answer 26

ohhhhhhhh, makes sense

Answer 27

something called equation on youer reply box :)

Answer 28

thanks! I think I got it now :)

Answer 29

your*

Answer 30

most welcome ^_^!

Answer 31

Just a suggestion mind you. the second term that is factored as:\[-5/y(y-x)\]

can be simplified by changing it to the following:\[+(5/(x-y)\]
This can be done by multiply by -1 twice, once changing the - to a plux making it and addition and then again changeing the y(y-x) to y(x+y) I think thats legal. Don't know if that will help or not

Answer 32

Is that legal?

Answer 33

Oooops Change the last line on the post 2nd above to read y(x-y)

Answer 34

hmm, it's true, it can be, but I'm not sure though, wouldn't that change the function completely?

Answer 35

I wondering too, but multiplying by -1 one twice is the same as multiplying by a +1 and theoretically shouldn't change it.

Answer 36

you have just answered the question in a much simpler way! thank you ^_^!

Answer 37

yes thank you!

Answer 38

:)