Answer:
Four steps of multiplying the rational expressions and their examples are given below
Factor the expression acting as the numerator and denominator of both functions
[tex]\frac{x+3}{x^2-3x}\cdot\frac{x}{x^2+9y+18} = \frac{(x+3)}{(x)(x-3)}\cdot\frac{x}{(x+6)(x+3)}[/tex]
Write both of the expression being multiplied as one expression
[tex]\frac{(x+3)}{(x)(x-3)}\cdot\frac{x}{(x+6)(x+3)}= \frac{(x+3)(x)}{(x)(x-3)(x+6)(x+3)}[/tex]
Simplify the rational expression by cutting out the common terms
[tex]\frac{(x+3)(x)}{(x)(x-3)(x+6)(x+3)} = \frac{1}{(x-3)(x+6)}[/tex]
Multiply any remaining factors in numerator or denominator.
[tex]\frac{1}{(x-3)(x+6)}=\frac{1}{x^2+3x-18}[/tex]
