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 $1$ .

$f (1.5) = \frac{3 \cdot 2.5 - (3 + 1.5)}{1.5 - 1}$

Multiply $3$ by $2.5$ .

$f (1.5) = \frac{7.5 - (3 + 1.5)}{1.5 - 1}$

Add $3$ and $1.5$ .

$f (1.5) = \frac{7.5 - 1 \cdot 4.5}{1.5 - 1}$

Multiply $- 1$ by $4.5$ .

$f (1.5) = \frac{7.5 - 4.5}{1.5 - 1}$

Simplify the expression.

Subtract $4.5$ from $7.5$ .

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

Subtract $1$ from $1.5$ .

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

Divide $3$ by $0.5$ .

$f (1.5) = 6$

The final answer is $6$ .

$6$

Step 3