Aufgaben:
8. Reduce the rational expression to lowest terms.
\( \frac{5 x^{2}+15 x^{3}}{12 x+36 w^{2}} = \)
a. \( \frac{5}{12} \quad \)
b. \( \frac{5 x^{2}+15 x^{3}}{12 x+36 x^{2}} \)
c. \( \frac{500}{12} \)
d. \( \frac{5+15 w^{3}}{12 x+36} \)
9. Perform the indicated operations and simplify the result. Leave the answer in factored form.
\( \frac{3 k-3}{x} \cdot \frac{\operatorname{los}^{2}}{4 x-4} = \)
a. \( \frac{2}{8 x} \)
b. \( \frac{9 x}{2} \)
c. \( \frac{10 x^{3}-16 x^{2}}{4 x^{2}-4 x} \)
d. \( \frac{12 x^{2}+24 x+12}{6 x^{3}} \)
10. Perform the indicated operations and simplify the result. Leave the answer in factored form.
\( \frac{x^{2}-7 x+12}{x^{2}-8 x+7} \cdot \frac{x^{2}-13 x+42}{x^{2}-14 x+40} = \)
a. \( \frac{\left(x^{2}-7 x+124\left(x^{2}-13 x+42\right)\right.}{\left(x^{2}-8 x+7\right)\left(x^{2}-14 x+40\right)} \)
b. \( \frac{(x-3)(x-6)}{(x-1)(x-10)} \)
c. \( \quad \frac{(x+3)(x+6)}{(x+1)(x+10)} \)
d. \( \quad \frac{(x-3)}{(x-10)} \)
