Question

Question 8 of 25 Which of the following is the quotient of the rational expressions shown here?

Answer 1

Answer:

  B.  (5x+5)/(x²-2x)

Step-by-step explanation:

As with numerical fractions, division by a rational expression is equivalent to multiplication by its reciprocal.

As a multiplication problem

  $\dfrac{5}{x-2}\div\dfrac{x}{x+1}=\dfrac{5}{x-2}\times\dfrac{x+1}{x}$

Product of rational expressions

As with numerical fractions, the product is the product of numerators, divided by the product of denominators.

  $=\dfrac{5(x+1)}{x(x-2)}=\boxed{\dfrac{5x+5}{x^2-2x}}$