Which of the following is equivalent to x1-x-1x when x < 0?

x1-x-1x = xxx-x-1x = xx-(x-1)x = x1x = x^2 = |x| Since x<0,|x|= -x

imc

algebra intermediate

Problem

Which of the following is equivalent to

\frac{x}{1 - \frac{x - 1}{x}}

when

x < 0

(A)

- x

(B)

x

(C)

1

(D)

\frac{x}{2}

Solution

\frac{x}{1 - \frac{x - 1}{x}} = \frac{x}{\frac{x}{x} - \frac{x - 1}{x}} = \frac{x}{\frac{x - ( x - 1 )}{x}} = \frac{x}{\frac{1}{x}} = x^{2} = ∣ x ∣

Since

x < 0, ∣ x ∣ = - x

Final answer