Question

30 points if you answer this question and please show work !

The domain for f(x) and g(x) is the set of all real numbers.
Let f(x) = x2 +x-20 and g(x) = x +5
Find f(x)/g(x)

Answer 1

`h(x)=(f(x))/(g(x))=(x^2+x-20)/(x+5)=(x^2+x+4x-4x-20)/(x+5)=\\\\\\= (x^2+5x-4x-20)/(x+5)=(x(x+5)-4(x+5))/(x+5)=((x+5)(x-4))/(x+5)=\\\\\\=\boxed{x-4}`

We see, that g(x) is in denominator, so:


`g(x)\\eq0\\\\x+5\\eq0\\\\\boxed{x\\eq-5}`

and the domain of
`h(x)` is the set of all real numbers without
`x=-5`.