Question

Which of the following is the quotient of the rational expressions shown here? x/x-1 / 1/x 1.

Answer 1

The quotient of the rational expressions is $\rm \dfrac{x^2-x}{x-1}$.

Given that

Rational Expression; $\rm \dfrac{x}{x-1}$ ÷$\rm \dfrac{1}{x+1}$

We have to determine

Which of the following is the quotient of the rational expressions shown here?

According to the question

Rational Expression; $\rm \dfrac{x}{x-1}$ ÷$\rm \dfrac{1}{x+1}$

Then,

The quotient of the rational expressions is,

$\rm \dfrac{x}{x-1}$ ÷$\rm \dfrac{1}{x+1}$

$\rm =\dfrac{x}{x-1} \times \dfrac{x+1}{1}\\ \\ =\dfrac{x(x-1)}{x\times 1}\\ \\ =\dfrac{x^2-x}{x-1}$

Hence, The quotient of the rational expressions is $\rm \dfrac{x^2-x}{x-1}$.

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