Mathematics

Problem

The function

h(x)=\frac{x^{2}-9}{x(x-3)^{2}}

contains a repeated linear factor in its denominator. (i) Factor the denominator of

h(x)

completely and identify the multiplicity of each factor. (ii) Find all real numbers that are excluded from the domain of

h

. (iii) Write the domain of

h

using interval notation. (iv) Describe verbally how the domain would be represented on a number line (do not draw the diagram).