Evaluate the Function f(-1.5)=(2t(t+1))/(t-1)-(3+t)/(t-1)

$f (- 1.5) = \frac{2 t (t + 1)}{t - 1} - \frac{3 + t}{t - 1}$

Step 1

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

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

Step 2

Simplify the result.

Combine fractions.

Remove parentheses.

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

Combine the numerators over the common denominator.

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

Simplify each term.

Multiply $2$ by $- 1.5$ .

$f (- 1.5) = \frac{- 3 ((- 1.5) + 1) - (3 - 1.5)}{- 1.5 - 1}$

Add $- 1.5$ and $1$ .

$f (- 1.5) = \frac{- 3 \cdot - 0.5 - (3 - 1.5)}{- 1.5 - 1}$

Multiply $- 3$ by $- 0.5$ .

$f (- 1.5) = \frac{1.5 - (3 - 1.5)}{- 1.5 - 1}$

Subtract $1.5$ from $3$ .

$f (- 1.5) = \frac{1.5 - 1 \cdot 1.5}{- 1.5 - 1}$

Multiply $- 1$ by $1.5$ .

$f (- 1.5) = \frac{1.5 - 1.5}{- 1.5 - 1}$

Simplify the expression.

Subtract $1.5$ from $1.5$ .

$f (- 1.5) = \frac{0}{- 1.5 - 1}$

Subtract $1$ from $- 1.5$ .

$f (- 1.5) = \frac{0}{- 2.5}$

Divide $0$ by $- 2.5$ .

$f (- 1.5) = 0$

The final answer is $0$ .

$0$

Step 3