Question

Which of the following is the quotient of the rational expressions shownbelow? Make sure your answer is in reduced form

Answer 1

The answer is C.

EXPLANATION :

From the problem, we have :

`(2x-1)/(x+1)/(3x^2)/(x^2+x)`

Note that the division symbol can be changed as a multiplication symbol in this manner :

`a/ b\rightarrow a*(1)/(b)`

We need just to take the reciprocal of the second expression.

Then :

`\begin{gathered} (2x-1)/(x+1)*(x^2+x)/(3x^2) \\ \\ \text{ Factor the second expression :} \\ \\ (2x-1)/(x+1)*(x(x+1))/(3x^2)=\frac{2x-1}{\cancel{x+1}}*\frac{\cancel{x}\cancel{(x+1)}}{3x^{\cancel{2}}} \\ \\ =(2x-1)*(1)/(3x) \\ \\ =(2x-1)/(3x) \end{gathered}`