Question

Please help with this problem.....2x-6 over x-1?? Its a fraction and the answer is 2 I just am lost on how to get there?

Answer 1

are you trying to solve\[\frac{2x-6}{x-1}=2\]

Answer 2

yes

Answer 3

well the 2 doesnt show up, my teacher told me thaths the answer. I have to find the common denominator and all that?

Answer 4

hmmm...then i;m lost.

let's start from the beginning.

Answer 5

what is the original problem?

Answer 6

ok thank you I will. what sign do you use for a fraction? on here?

Answer 7

i use the equation editor button...but you can also use parentheses to group the parts of the fraction together

Answer 8

such as 2x-(6/x-1) would be\[2x-\frac{6}{x-1}\]

Answer 9

ok so , (2x-6)/(x-1) - (4)/(1-x)

Answer 10

ahhh..ok. i see now.

Answer 11

sorry that took a while

Answer 12

\[\frac{2x-6}{x-1}-\frac{4}{1-x}\]?

Answer 13

yess yess

Answer 14

:D ok...here goes

Answer 15

:) lets see it!

Answer 16

you understand that x-1 = -1(1-x), right?

Answer 17

yes I got that

Answer 18

ok...so i'm going to change the second fraction so that the denominator looks like the first fraction. (get a common denominator)

Answer 19

ok which is x/1

Answer 20

\[\frac{2x-6}{x-1}-\frac{4}{1-x}=\frac{2x-6}{x-1}-\frac{4}{-(x-1)}\]

Answer 21

good so far?

Answer 22

yes except, when u have to divide by the -1 you only do the denominator?

Answer 23

it doesn't matter...i can put the negative on top, bottom, or out in front.

Answer 24

ok got that then, next step is where I get lost

Answer 25

In fact, I'm going to move it out in front which gives me me minus a negative...which is addition, right?

Answer 26

so we have\[\frac{2x-6}{x-1}-(-\frac{4}{x-1}) = \frac{2x-6}{x-1}+\frac{4}{x-1}\]

Answer 27

ok so now its addition, got it

Answer 28

\[=\frac{2x-6+4}{x-1}\]

Answer 29

since the denominators are the same...right?

Answer 30

yes right

Answer 31

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

Answer 32

and as they say in the army..."HOOAH! :)

Answer 33

yes right

Answer 34

how do you get the 2(x-1)/(x-1)? Andd yess HOOAH!

Answer 35

but as we in the Navy say to our army brothers..."Hooah, Shipmate!"

Answer 36

i factored out a 2 from both terms in the numerator...

Answer 37

it's distribution in reverse.

Answer 38

2(x-1) = 2x-2, right?

Answer 39

ohh ok thank you life saver :) got it! Nicee Navy/army lingo

Answer 40

my pleasure. :)