Evaluate Using the Given Value (a-(2a-1)/a)/((1-a)/(3a)) if a=-1.5

$\frac{a - \frac{2 a - 1}{a}}{\frac{1 - a}{3 a}}$ if $a = - 1.5$

Step 1

Replace the variable $a$ with $- 1.5$ in the expression.

$\frac{(- 1.5) - \frac{2 (- 1.5) - 1}{- 1.5}}{\frac{1 - (- 1.5)}{3 (- 1.5)}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$(- 1.5 - \frac{2 (- 1.5) - 1}{- 1.5}) \frac{3 (- 1.5)}{1 - (- 1.5)}$

Step 3

Multiply $3$ by $- 1.5$ .

$(- 1.5 - \frac{2 (- 1.5) - 1}{- 1.5}) \frac{- 4.5}{1 - (- 1.5)}$

Step 4

Simplify the denominator.

Multiply $- 1$ by $- 1.5$ .

$(- 1.5 - \frac{2 (- 1.5) - 1}{- 1.5}) \frac{- 4.5}{1 + 1.5}$

Add $1$ and $1.5$ .

$(- 1.5 - \frac{2 (- 1.5) - 1}{- 1.5}) \frac{- 4.5}{2.5}$

Step 5

Simplify terms.

Simplify each term.

Simplify the numerator.

Multiply $2$ by $- 1.5$ .

$(- 1.5 - \frac{- 3 - 1}{- 1.5}) \frac{- 4.5}{2.5}$

Subtract $1$ from $- 3$ .

$(- 1.5 - \frac{- 4}{- 1.5}) \frac{- 4.5}{2.5}$

Divide $- 4$ by $- 1.5$ .

$(- 1.5 - 1 \cdot 2.\overline{6}) \frac{- 4.5}{2.5}$

Multiply $- 1$ by $2.\overline{6}$ .

$(- 1.5 - 2.\overline{6}) \frac{- 4.5}{2.5}$

Simplify the expression.

Subtract $2.\overline{6}$ from $- 1.5$ .

$- 4.1\overline{6} (\frac{- 4.5}{2.5})$

Divide $- 4.5$ by $2.5$ .

$- 4.1\overline{6} \cdot - 1.8$

Multiply $- 4.1\overline{6}$ by $- 1.8$ .

$7.5$