I'm following example 8.47 from the OpenStax book Elementary Algebra.
When trying to create a common denominator it is sometimes necessary to handle opposites on either side of an equation.
In the example, $(2-n)$ needs to be converted to $(n-2)$ as follows:
$$-\frac{(n+3)}{(2-n)}$$
To do this we multiply the numerator and denominator by $-1$.
$$-\frac{(-1)(n+3)}{(-1)(2-n)}$$
Which gives:
$$+\frac{(n+3)}{(n-2)}$$
I understand why the denominator changes but not why the numerator stays the same and the sign of the whole expression changes. Could someone explain this, please?
Don't forget the minus sign 'outside' the fraction disappeared as well:
$$-\frac{(-1)(n+3)}{(-1)(2-n)}=$$ $$-1\frac{(-1)(n+3)}{(-1)(2-n)}=$$ $$\frac{-1\cdot-1\cdot(n+3)}{(-1)(2-n)}=$$ $$\frac{(n+3)}{(-1)(2-n)}=$$ $$\frac{(n+3)}{(n-2)}$$