Answer:
[tex] \dfrac{z + 3}{z} [/tex]
Step-by-step explanation:
[tex] \dfrac{z^2 + 11z + 18}{z^2 + 14 z + 45} \times \dfrac{z^2 + 8z + 15}{z^2 + 2z} = [/tex]
Multiply the numerators. Multiply the denominators.
[tex] = \dfrac{(z^2 + 11z + 18)(z^2 + 8z + 15)}{(z^2 + 14 z + 45)(z^2 + 2z)} [/tex]
Factor every polynomial.
[tex] = \dfrac{(z + 2)(z + 9)(z + 5)(z + 3)}{(z + 5)(z + 9)z(z + 2)} [/tex]
Divide the numerator and denominator by equal factors.
[tex] = \dfrac{z + 3}{z} [/tex]
