Question

How do I simplify this? https://secure.aleks.com/alekscgi/x/math2htgif.exe/NM?%25ps8%25ps8%25ps8%25ps8%3Fal%7B%3D%3Fal%7B%3D1%3Flufq%3D%7B%23%2E%232%3F%2Cal%7B%3D%23%28%231%3F%2Cal%7B%3D%25ps8%25ps8%25ps8%25ps8%3Flufq%3D%3Fal%7B%3D%3Fal%7B%3D1%3Flufq%3D%7B%23%28%232%3F%2Cal%7B%3D%23%2E%231%3F%2Cal%7B%3D

Answer 1

\[\frac{\dfrac{2}{x-1}+2}{\dfrac{2}{x-1}-2}\]

Answer 2

multiply the numerator and the denominator by (x-1)

Answer 3

So would the answer be -1?

Answer 4

\[=\frac{{2}+2(x-1)}{{2}-2(x-1)}\\
=\]

Answer 5

I mean would the answer be 1? cause it's 2x/2x in the end

Answer 6

wait a minute

Answer 7

\[=\frac{{2}+2(x-1)}{{2}-2(x-1)}=\frac{{2}+2x-2}{{2}-2x+2}\\
=\frac{2x}{4-2x}=\]

Answer 8

So the final answer is \[\frac{ 2x }{ 4-2x }\] ? since you can't simplify any further

Answer 9

but there is still a common factor

Answer 10

The common factor is 2x and -2x but how do you simplify it when theres the 4-2x?

Answer 11

the common factor is just 2

Answer 12

So the final answer is 2x/2x = 1?

Answer 13

what happened to the four?

Answer 14

Wouldn't you do 4-2 = 2? or How would i simplify it further?

Answer 15

\[\frac{ 2x }{ 4-2x }=\frac{ 2(x) }{ 2(2-x) }=\frac{ \cancel 2(x) }{ \cancel2(2-x) }\]

Answer 16

How do you go from \[\frac{ 2x }{ 4-2x }\] to \[\frac{ 2(x) }{ 2(2-x) }\]?

Answer 17

factoring out a factor of 2

4=(2)(2)

-2x=(2)(-x)


4-(2x)=(2)[2]-(2)[x]=2[2-x]