Question

x/x-2+3=2/x-2

Answer 1

I assume it is this:

\[\frac{x}{x-2} + 3 = \frac{2}{x-2}\]

Answer 2

If that is correct, then subtract \(\large \frac{x}{x-2}\) from both sides

Answer 3

You should end up with

\[3 = \frac{2}{x-2} - \frac{x}{x-2}\]

Answer 4

Now combine fractions on the right side to get

\[3 = \frac{2 - x}{x-2}\]

Answer 5

You can re-write 3 as a fraction; Then you'll have

\[\frac{3}{1} = \frac{2 - x}{x-2}\]

Now all you have to do is cross multiply to get

\[3(x-2) = 1(2-x)\]

You should be able to finish solving for x from there.

Answer 6

ah ok let me try

Answer 7

but what is the number one thing i shopuld remember when doing this kind of problems

Answer 8

Well, each problem is different and there are different ways of doing them.

Answer 9

But I am going to make a slight change to the fraction I created above

Answer 10

ok

Answer 11

It can be re-written as:

\[3 = -\frac{x-2}{x-2}\]

Answer 12

And as we both know, anything over itself equals 1 so:

\(3 = -1\)

But we know that isn't true so

\(3 \ne -1\)

Answer 13

So there is no solution to this problem

Answer 14

ok

Answer 15

If you continued solving it the other way, you would get x = 2, but we can't have 2 in the denominator of the fraction.

Answer 16

So either way, no solution.

Answer 17

ok i did it i got 2 but my book says i should get no solution so it"s confusing

Answer 18

why cant we have 2 in the denominator explain that please

Answer 19

If you had 2 in the denominator, then you would have a zero denominator, which is not possible

Answer 20

You cannot have a fraction with \(\frac{2}{0}\) or \(\frac{x}{0}\)

Answer 21

Fractions with zero in the denominator are not defined by mathematics.

Answer 22

ah ok i got you now thank you so much for your explanation and your help