multiplying by the reciprocal

multiplying

the reciprocal

dividing by the reciprocal

$$\frac{x}{2y}\cdot\frac{4}{xy}$$  

$$\frac{x}{2y}\cdot\frac{xy}{4}$$  

$$\frac{2y}{x}\cdot\frac{4}{xy}$$  

$$\frac{2y}{x}\cdot\frac{xy}{4}$$  

$$\frac{x^2-y^2}{x^2+y^2}\cdot\frac{1}{\left(x+y\right)}$$  

$$\frac{x^2-y^2}{x^2+y^2}\cdot\frac{\left(x+y\right)}{1}$$  

$$\frac{18}{x^2-25}\cdot\frac{x+5}{24}$$  

$$\frac{x^2-25}{18}\cdot\frac{24}{x+5}$$  

Factor

Cross off like terms

Multiply the numerators

Multiply the denominators

$$\frac{x^2+3x-10}{2x+6}\cdot\frac{x^2-4}{x^2-x-12}$$  

$$\frac{x^2+3x-10}{2x+6}\cdot\frac{x^2-x-12}{x^2-4}$$  

$$\frac{\left(x+5\right)\left(x-2\right)}{2\left(x+3\right)}\cdot\frac{\left(x-4\right)\left(x+3\right)}{\left(x-2\right)\left(x+2\right)}$$  

$$\frac{\left(x+5\right)\left(x-2\right)}{2x+6}\cdot\frac{\left(x-4\right)\left(x+3\right)}{\left(x-2\right)\left(x+2\right)}$$  

$$\frac{\left(x+5\right)\left(x-2\right)}{2\left(x+3\right)}\cdot\frac{\left(x-2\right)\left(x+2\right)}{\left(x-4\right)\left(x+3\right)}$$  

$$\frac{\left(x+5\right)\left(x-4\right)}{2\left(x+2\right)}$$  

$$\frac{x^2-20}{2x-4}$$  

$$\frac{\left(x+5\right)}{\left(x+2\right)}$$  

$$-\frac{x-3}{x+3}$$  

$$\frac{x-3}{x+3}$$  

$$-1$$  

$$1$$