Mathematics

Problem

51. Revisit Example 4 Consider the following equation, which we solved in Example 4.

\frac{x-3}{x}+\frac{3}{x+2}+\frac{6}{x^{2}+2 x}=0

Let

f(x)=\frac{x-3}{x}+\frac{3}{x+2}+\frac{6}{x^{2}+2 x}

. (a) Combine the fractions in

f(x)

but do not reduce to lowest terms. (b) What is the domain of

f

? (c) Write

f

as a piecewise-defined function. (d) Writing to Learn Graph

f

and explain how the graph supports your answers in (b) and (c).