Question

select the correct answer from each drop-down menu.

consider this expression.

\\\frac{3}{x-2} + \frac{x-2}{x^2-4x+4}\\

the simplest form of the expression has choose an answer in the numerator and choose an answer in the denominator.

Explanation:

Factor the denominators

$$ x^2 - 4x + 4 = (x - 2)^2 $$

Rewrite and find a common denominator

$$ \frac{3}{x - 2} + \frac{x - 2}{(x - 2)^2} = \frac{3}{x - 2} + \frac{1}{x - 2} $$

Combine the terms

$$ \frac{3 + 1}{x - 2} = \frac{4}{x - 2} $$

Answer:

Consider this expression.

$$\frac{3}{x-2} + \frac{x-2}{x^2-4x+4}$$

The simplest form of the expression has <blank>4</blank> in the numerator and <blank>\(x-2\)</blank> in the denominator.