Question

Show all work to simplify 2 over x + 2 over x minus 1 - 2 over x minus 2. Use complete sentences to explain how to simplify this expression

Answer 1

so is the question

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

Answer 2

ok... so you need a common denominator

1st term is

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

2nd term is

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

and the last term is

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

so you will have

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

so you need to distribute \[\frac{2x^2 - 6x + 4 + 2x^2 - 4x - 2x^2 + 2x}{x^3 - 3x^2 + 2x}\]

lastly just collect like terms.

Answer 3

thank you so much!