Question

rationalize the denomenator

Answer 1

the rational conjugate of the denominator is \[\sqrt x+2\]

so multiply your whole expression by \(1 =\dfrac{\sqrt x+2}{\sqrt x+2}\)

i.e.

\[\frac{x^2-16}{\sqrt x-2}\\=\frac{x^2-16}{\sqrt x-2}\times1\\
=\frac{x^2-16}{\sqrt x-2}\times\dfrac{\sqrt x+2}{\sqrt x+2}\]

when you now multiply the numerator and denominators, the denominator will become rational

Answer 2

numerators* and denominators

Answer 3

When you multiply the denominator make use of the identity:
\((a+b)(a-b) = a^2 - b^2\)

Also, before multiplying the numerator, factor \(x^2 - 16\) once again making use of the identity \(a^2 - b^2 = (a+b)(a-b)\). Cancel out any common factors and then multiply.