Question

Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.

Answer 1

Answer:

5 - x

Step-by-step explanation:

Given:

$f(x)=25-x^2$

$g(x)=x+5$

$\begin{aligned}\left(\dfrac{f}{g}\right)(x) & = \dfrac{f(x)}{g(x)}\\\\ & = \dfrac{25-x^2}{x+5}\\\\& = \dfrac{(5-x)(5+x)}{(x+5)}\\\\& = \dfrac{(5-x)(x+5)}{(x+5)}\\\\& = 5-x\end{aligned}$

Answer 2

Answer:

$\sf \left(\dfrac{f}{g}\right)(x)=5-x$

Step-by-step explanation:

Given functions:

f(x) = 25 - x²

g(x) = x + 5

Difference of Perfect Squares rule: a² - b² = (a + b)×(a - b)

1. Rewrite function f(x) using the rule:

5 × 5 = 25 ⇒ 5²

x × x = x²

f(x) = 5² - x² ⇒ f(x) = (5 + x)×(5 - x)

2. Divide and simplify:

$\sf\left(\dfrac{f}{g}\right)(x) =\dfrac{f(x)}{g(x)}\\\\\left(\dfrac{f}{g}\right)(x)=\dfrac{(5 + x)(5 - x)}{x+5}\\\\\left(\dfrac{f}{g}\right)(x)=5-x$