Question

Simplify the difference quotient for the function given below, if x does not equal a.
f(x)-f(a)/x-a for f(x)=sqrt(x-31)

Answer 1

\[
\frac{\left(\sqrt{x-31}-\sqrt{a-31}\right)
\left(\sqrt{a-31}-\sqrt{x-31}\right)}{(x-a)
\left(\sqrt{a-31}-\sqrt{x-31}\right)}
\]

Answer 2

\[
\frac{\left(\sqrt{x-31}-\sqrt{a-31}\right)
\left(\sqrt{a-31}-\sqrt{x-31}\right)}{(x-a)
\left(\sqrt{a-31}-\sqrt{x-31}\right)}=\\\frac{x-a}{(x-a
)
\left(\sqrt{a-31}-\sqrt{x-31}\right)}=\frac{1}{\sqrt{
a-31}-\sqrt{x-31}}
\]

Answer 3

It's \[\frac{ 1 }{ \sqrt{x-31}+\sqrt{a-31} }\]
Thank you though!