Question

1. $\frac{8x^{3}-72x^{2}}{8x^{2}} div \frac{x^{2}-13x+36}{7}$

Explanation:

Step1: Rewrite division as multiplication

$\frac{8x^3 - 72x^2}{8x^2} \times \frac{7}{x^2 - 13x + 36}$

Step2: Factor numerator of first fraction

$\frac{8x^2(x - 9)}{8x^2} \times \frac{7}{x^2 - 13x + 36}$

Step3: Cancel common terms

$\frac{\cancel{8x^2}(x - 9)}{\cancel{8x^2}} \times \frac{7}{x^2 - 13x + 36} = (x - 9) \times \frac{7}{x^2 - 13x + 36}$

Step4: Factor quadratic denominator

$(x - 9) \times \frac{7}{(x - 4)(x - 9)}$

Step5: Cancel common binomial term

$\frac{(x - 9) \times 7}{(x - 4)(x - 9)} = \frac{7}{x - 4}$

Answer:

$\frac{7}{x - 4}$ (where $x
eq 0, 4, 9$)