Multiplicación y División de Fracciones

2. Halla el producto de ${\displaystyle \frac{ab-b^2}{a+b}}\times {\displaystyle \frac{ab+b^2}{a^2-b^2}}$. $\frac{ab-b^2}{a+b}\times \frac{ab+b^2}{a^2-b^2}=\frac{b(a-b)}{(a+b)}\times \frac{b(a+b)}{(a-b)(a+b)}=\frac{b^2}{a+b}.$

3. Halla el cociente de ${\displaystyle \frac{ab}{(a-b{)}^2}}÷{\displaystyle \frac{ac}{a^2-b^2}}$.

$$\begin{gathered} \frac{ab}{(a-b{)}^2}÷\frac{ac}{a^2-b^2}\&=\frac{ab}{(a-b)(a-b)}\times \frac{(a-b)(a+b)}{ac} \\ \&=\frac{b(a+b)}{c(a-b)}. \end{gathered}$$

4. Encuentra el resultado de ${\displaystyle \frac{1}{x}}\times {\displaystyle \frac{x^2-1}{x^2-4x-5}}÷{\displaystyle \frac{x^2+2x-3}{x^2-25}}$.

$$\begin{gathered} \&\frac{1}{x}\times \frac{x^2-1}{x^2-4x-5}÷\frac{x^2+2x-3}{x^2-25} \\ \&=\frac{1}{x}\times \frac{x^2-1}{x^2-4x-5}\times \frac{x^2-25}{x^2+2x-3} \\ \&=\frac{1}{x}\times \frac{(x-1)(x+1)}{(x-5)(x+1)}\times \frac{(x-5)(x+5)}{(x+3)(x-1)} \\ \&=\frac{x+5}{x(x+3)}. \end{gathered}$$

Ejercicio 49.

Expresa en su forma más simple:

1. ${\displaystyle \frac{15a^2}{7b^2}}\times {\displaystyle \frac{28ab}{9a^{3}c}}$.

2. ${\displaystyle \frac{3x^2{y}^2{z}^3}{4a^2{b}^2{c}^2}}\times {\displaystyle \frac{8a^3{b}^2{c}^2}{9x^{2}y{z}^3}}$.

3. ${\displaystyle \frac{5m^2{n}^2{p}^4}{3x^{2}y{z}^3}}\times {\displaystyle \frac{21xy{z}^2}{20m^2{n}^2{p}^2}}$.

4. ${\displaystyle \frac{16a^4{b}^2{c}^3}{21m^2{x}^3{y}^4}}\times {\displaystyle \frac{3m^3{x}^3{y}^4}{8a^2{b}^2{c}^2}}$.

5. ${\displaystyle \frac{2a}{bc}}\times {\displaystyle \frac{3b}{ac}}\times {\displaystyle \frac{5c}{ab}}$.

6. ${\displaystyle \frac{2a^3}{3bc}}\times {\displaystyle \frac{3b^3}{5ac}}\times {\displaystyle \frac{5c^3}{2ab}}$.

7. ${\displaystyle \frac{5ab{c}^3}{3x^2}}÷{\displaystyle \frac{10a{c}^3}{6b{x}^2}}$.

8. ${\displaystyle \frac{x^2-a^2}{x^2-4a^2}}\times {\displaystyle \frac{x+2a}{x-a}}$.

9. ${\displaystyle \frac{x^2{y}^2+3xy}{4c^2-1}}\times {\displaystyle \frac{2c+1}{xy+3}}$.

10. ${\displaystyle \frac{a^2-100}{a^2-9}}\times {\displaystyle \frac{a-3}{a-10}}$.

11. ${\displaystyle \frac{9x^2-4y^2}{x^2-4}}\times {\displaystyle \frac{x+2}{3x-2y}}$.

12. ${\displaystyle \frac{25a^2-b^2}{16a^2-9b^2}}÷{\displaystyle \frac{5a-b}{4a-3b}}$.

13. ${\displaystyle \frac{x^2-49}{(a+b{)}^2-c^2}}÷{\displaystyle \frac{x+7}{(a+b)-c}}$.