Question

How do you simplify `(5p-10)/(2-p)`?

Answer 1

`-5`

Explanation:

Consider `5p-10`

Factor out the 5 giving: `5(p-2)`

Notice that the `p-2` is the other way round to that in the denominator. We can 'play' with this by 'adjusting' signs

Mathematically you can change things into any form you wish as long as you incorporate something that will take everything back to their original values.

Lets multiply `5(p-2)` by `(-1)` giving:`-5(p-2)`
But this changes the values so lets make adjustments so that when we multiply by `(-5)` we end up with the original `5p-10`

Write `5(p-2)` as `-5(2-p)`

Now it matches the denominator and we can cancel out

`(-5(2-p))/(2-p) color(white)("ddd")=color(white)("ddd") (-5)xx(2-p)/(2-p)color(white)("ddd") =color(white)("ddd") -5`