Answer:
1). [tex]\frac{2}{(x+1)}[/tex]
2). [tex]\frac{x^2}{2(x+1)}[/tex]
Step-by-step explanation:
For multiplication of the rational expressions,
[tex]\frac{x}{(x+1)}\times \frac{2}{x}[/tex]
= [tex]\frac{2x}{x(x+1)}[/tex]
= [tex]\frac{2}{(x+1)}[/tex]
For division of the rational expressions,
[tex]\frac{x}{(x+1)}\div \frac{2}{x}[/tex]
= [tex]\frac{x}{(x+1)}\times \frac{x}{2}[/tex]
= [tex]\frac{x^2}{2(x+1)}[/tex]
[When the divisor is a rational expression or a rational number, we change the sign from division to multiplication and reciprocate or flip the fraction.
This is applicable for division of the rational expressions only].
