Question

simplify.

\\\frac{p^2 - 49}{p^2 - 14p + 49}\\

Explanation:

Factor the numerator

Using the Difference of Squares knowledge point

$$ p^2 - 49 = (p - 7)(p + 7) $$

Factor the denominator

Using the Polynomial Factoring knowledge point

$$ p^2 - 14p + 49 = (p - 7)^2 = (p - 7)(p - 7) $$

Simplify the rational expression

We divide out the common factor \(p - 7\) from both the numerator and the denominator, assuming \(p
eq 7\):

$$ \frac{(p - 7)(p + 7)}{(p - 7)(p - 7)} = \frac{p + 7}{p - 7} $$

Answer:

Simplify.

$$\frac{p^2 - 49}{p^2 - 14p + 49} =$$

<blank>\(\frac{p + 7}{p - 7}\)</blank>