Question

Show all work to simplify (x/2)-(2/(x-1))+(2/(x-2)) and list the restrictions

Answer 1

Hint: x = 1 and x = 2 will make the denominators zero

Answer 2

is the common denominator x(x-2)?

Answer 3

If x(x-2) was the common denominator, you would be able to use it to combine each fraction. But there are THREE fractions, and THREE different denominators, which means there will be THREE numbers multiplied together to form the LCM. x(x-2) represents only two numbers

Answer 4

oh, then whats the lowest common denominator?

Answer 5

In this case, LCM = LCD

Answer 6

and what number is that? because i rele dont understand

Answer 7

Hmmm. You have three different fractions, each with three different denominators, yet the denominators of each must be the same before you can combine them. What if you had

\(\frac{1}{2} + \frac{2}{3} + \frac{3}{5}\)

Answer 8

What would you do in this case?

Answer 9

you multiply all of them
but that would be 2x^2+3x+2

Answer 10

you multiply all of them
but that would be 2x^2+3x+2

Answer 11

Yes, but guess what? The denominators would be the same and you would be able to combine them.

Answer 12

Did you multiply 2(x-1)(x-2) ?

Answer 13

i messed up with writing it it should be (2/x)-(2/x-1)+(2/x-2)

Answer 14

No, you should write it like this 2/x - 2/(x-1) + 2/(x-2) to distinguish the numerator from the denominator.

Answer 15

That becomes

\(\large\frac{2}{x} - \frac{2}{x-1} + \frac{2}{x-2} \)

Answer 16

im now really confused, what is the LCD

Answer 17

The LCD is x(x-1)(x-2)