Question

Write in simplest form

Answer 1

f(x)=25-x^2
g(x)=x+5
(f/g)(x)=?

(f/g)(x)=f(x)/g(x)=(25-x^2)/(x+5)

Factoring the numerator f(x), using a^2-b^2=(a+b)(a-b);
with a^2=25 and b^2=x^2:
f(x)=25-x^2=[sqrt(25)+sqrt(x^2)] [sqrt(25)-sqrt(x^2)]
f(x)=25-x^2=(5+x)(5-x)
f(x)=25-x^2=(x+5)(5-x)

(f/g)(x)=f(x)/g(x)=(x+5)(5-x)/(x+5)

Simplifying for x+5 different of zero:
(f/g)(x)=5-x

Answer: (f/g)(x) = 5-x

Answer 2

If f(x)=25-x^2 and g(x)=x+5 what is (f/g)(x)=?

The answer would be (f/g)(x) = 5-x

Solution:
(f/g)(x)=f(x)/g(x)=(25-x^2)/(x+5)So, a^2=25 and b^2=x^2:f(x)=25-x^2=[sqrt(25)+sqrt(x^2)] [sqrt(25)-sqrt(x^2)]f(x)=25-x^2=(5+x)(5-x)f(x)=25-x^2=(x+5)(5-x)(f/g)(x)=f(x)/g(x)
=(x+5)(5-x)/(x+5)
Simplify:=(f/g)(x)
=5-x