## anonymous one year ago 24. Simplify the complex fraction. (5x^3/x+2)/30x^2/x+3) A) x(x+3)/6(x+2) B) 6x/ (x+2)(x+3) C) 150x^5/(x+2)(x+3) D) x+3/2 25. Divide the following rational expression, 16z^5 - 12z^4 + 8z^3 - 6z/2z^2 A) 8z^3 - 6z^2 + 8z - 3z B) 8z^3 - 6z^2 + 4z - 3/z C) 8z^3 + 6z^2 + 8z + 3z D) 10z^5 - 3

1. Vocaloid

@Directrix I'm about to get some sleep, would you mind taking over?

2. anonymous

$\large \frac{\dfrac{5x^3}{x+2}}{\dfrac{30x^2}{x+3}}$ Remember, when you're dividing by 2 fractions, follow this rule: $\large \frac{\frac{a}{b}}{\frac{c}{d}} \implies \frac{a}{b} \cdot \frac{d}{c}$

3. anonymous

therefore, $$\frac{\dfrac{5x^3}{x+2}}{\dfrac{30x^2}{x+3}}$$ becomes...$=\frac{5x^3}{x+2} \cdot \frac{x+3}{30x^2}$

4. anonymous

Now we just cross cancel like terms, $\frac{\color{red}{5}\color{blue}{x^3}}{x+2} \cdot \frac{x+3}{\color{red}{30}\color{blue}{x^2}}$

5. anonymous

For your second problem: $$\dfrac{16z^5 - 12z^4 + 8z^3 - 6z}{2z^2}$$ Divide each term in the numerator by the term in the denominator. $\frac{\color{red}{16}\color{blue}{z^5}}{\color{red}{2}\color{blue}{z^2}} -\frac{\color{red}{12}\color{blue}{z^4}}{\color{reD}{2}\color{blue}{z^2}}+\frac{\color{red}{8}\color{blue}{z^3}}{\color{red}{2}\color{blue}{z^2}}-\frac{\color{red}{6}\color{blue}{z}}{\color{red}{2}\color{blue}{z^2}}$

6. anonymous

@Jhannybean Thanks, I've completed them. :)

7. anonymous

Np :)