Question

simplify to a single fraction:
((x/x-1)+1)/((x+2)/x)

Answer 1

\[\left(\frac{x}{x+1}+1 \right)\div \frac{(x+2)}{x}\]
this?

Answer 2

yes.

Answer 3

(2x + 1)/(x+1) times x / (x + 2)

Answer 4

x(2x+1) / (x+1)(x+2)

Answer 5

wait....
am i multiplying (2x + 1)/(x+1) times x / (x + 2) to the original fraction??

Answer 6

yes (2x + 1)/(x + 1) is simplification of (1/(x+1) + 1) and since you're dividing by x / x + 2 you multiply by x + 2 / 2

Answer 7

do you get it?

Answer 8

soo it would be
((x/x-1)+1)/((x+2)/x) * (2x + 1)/(x+1) times x / (x + 2)
??

Answer 9

no where you have the * sign should be \[= equal\] to: The expressions are equivalent but in simplified form

Answer 10

((x/x-1)+1)/((x+2)/x) = (2x + 1)/(x+1) times x / (x + 2)

Answer 11

[x(2x+1)]/[(x+1)(x+2)] is your answer

Answer 12

ok i see... and then i would cancel out the x+2 and x correct?

Answer 13

No, you can only cancel out when you have same terms, x + 2 and x are different terms so you can't cancel them out. That answer will be as simplified as you can get the expression

Answer 14

so then what would i cancel out in order to simplify it?

Answer 15

Well in this case you can't cancel anything out it is already simplified tot he lowest form: [x(2x+1)]/[(x+1)(x+2)]

Answer 16

oh i see.. and what did u do in order to get that?
sorry if im asking so many questions.... i just wanna understand it.

Answer 17

Okay that's fine when you have an algebraic expression like that it is imperative to simplify both before you perform any arithmetic operation..so this was your question ((x/x-1)+1)/((x+2)/x) and we have to simplify this to a single fraction.

Answer 18

First of all we take : [(x/(x-1) + 1] = x/(x-1) + (x - 1)/(x - 1) =
2x - 1 / x -1..right?

Answer 19

right...

Answer 20

So know we have [(2x-1)/(x-1)] / [(x+2)/x]
[(2x-1)/(x-1)] x [x/(x+2)]

Answer 21

Answer = [x(2x-1)]/[(x-1)(x+2)]

Answer 22

OH! i get it now. thank you!!

Answer 23

Great! You're welcome!