Question

When f(x)=25-x^2 and g(x)= x+5, (f/g)(x)=___?

If f(x)=25-x^2 and g(x)=x+5, what is (f/g)(x)? Write your answer in simplest form.
When f(x)=25-x^2 and g(x)= x+5, (f/g)(x)=

Answer 1

`5-x`

Explanation:

`(f/g) x = f(x)/g(x)`

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

difference of two squares identity: `a^2 - b^2 = (a+b)(a-b)`

`25 - x^2 = 5^2 - x^2`
`= (5+x)(5-x)`

`g(x) = x+5 or 5+x`

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

`= (5-x)/1 = 5-x`