Question

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

Answer 1

ANSWER :

The answer is C.

EXPLANATION :

From the problem, we have :

$\frac{2x-1}{x+1}\div\frac{3x^2}{x^2+x}$

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

$a\div b\rightarrow a\times\frac{1}{b}$

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

Then :

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