Question

Show all work to simplify 2/x - 2/x-1 + 2/x-2 . Use complete sentences to explain how to simplify this expression. Remember to list all restrictions.

Answer 1

multiply each fraction by the common denominator, x(x-1)(x-2)

Answer 2

2/(x-1) is right correct? not (2/x) - 1

Answer 3

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

Answer 4

oh woops, i typed it wrong, it is 2/x + 2/x+1 - 2/x+2

Answer 5

use parenthesis

Answer 6

you wrote
\[\frac{ 2 }{ x } +1\]

Answer 7

2/(x+1)

Answer 8

is
\[\frac{ 2 }{ x+1 }\]

Answer 9

@ookay: You mean this?

\(\dfrac{ 2 }{ x } + \dfrac{ 2 }{ x + 1} - \dfrac{ 2 }{ x+2 }\)

Answer 10

yes @mathstudent55

Answer 11

Step 1: Find the LCD.
What is the LCD?

Answer 12

the lcd is x? im not too sure

Answer 13

LCD is: \(x(x + 1)(x + 2)\)

\(\dfrac{ 2 }{ x }\color{red}{\times \dfrac{x + 1}{x + 1} \times \dfrac{x + 2}{x + 2}} + \dfrac{ 2 }{ x + 1} \color{red}{\times \dfrac{x}{x} \times \dfrac{x +2}{x +2}} -
\dfrac{ 2 }{ x+2 }\color{red}{\times \dfrac{x }{x } \times \dfrac{x + 1}{x + 1}} \)

Answer 14

\(=\dfrac{ 2(x + 1)(x + 2) + 2(x)(x + 2) - 2(x)(x + 1) }{x(x + 1)(x + 2) } \)

Answer 15

Now you need to multiply out the numerator and combine like terms.

Answer 16

how would you do this? sorry

Answer 17

\(=\dfrac{ 2(x^2 + 2x + x + 2) + 2x^2 + 4x - 2x^2 -2x }{x(x + 1)(x + 2) }\)

\(=\dfrac{ 2x^2 + 6x + 4 + 2x^2 + 4x - 2x^2 -2x }{x(x + 1)(x + 2) }\)

\(=\dfrac{ 2x^2 + 8x + 4}{x(x + 1)(x + 2) }\)

\(=\dfrac{ 2(x^2 + 4x + 2)}{x(x + 1)(x + 2) }\)