Question

divide.
$(6yx - 15y^{4}x^{2})\div(-2y^{4}x^{2})$
simplify your answer as much as possible.

Explanation:

Step1: Split the division into two terms

$\frac{6yx - 15y^4x^2}{-2y^4x^2} = \frac{6yx}{-2y^4x^2} - \frac{15y^4x^2}{-2y^4x^2}$

Step2: Simplify the first fraction

Cancel common factors: $\frac{6}{-2} \cdot \frac{y}{y^4} \cdot \frac{x}{x^2} = -3 \cdot y^{1-4} \cdot x^{1-2} = -3y^{-3}x^{-1} = -\frac{3}{x y^3}$

Step3: Simplify the second fraction

Cancel common factors: $\frac{-15}{-2} \cdot \frac{y^4}{y^4} \cdot \frac{x^2}{x^2} = \frac{15}{2} \cdot 1 \cdot 1 = \frac{15}{2}$

Step4: Combine the results

Combine the simplified terms

Answer:

$-\frac{3}{x y^3} + \frac{15}{2}$