Algebra Examples

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

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.

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Step 2.1

Combine fractions.

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Step 2.1.1

Remove parentheses.

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

Step 2.1.2

Combine the numerators over the common denominator.

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

Step 2.2

Simplify each term.

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Step 2.2.1

Multiply $2$ by $1.5$ .

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

Step 2.2.2

Add $1.5$ and $1$ .

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

Step 2.2.3

Multiply $3$ by $2.5$ .

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

Step 2.2.4

Add $3$ and $1.5$ .

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

Step 2.2.5

Multiply $- 1$ by $4.5$ .

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

Step 2.3

Simplify the expression.

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Step 2.3.1

Subtract $4.5$ from $7.5$ .

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

Step 2.3.2

Subtract $1$ from $1.5$ .

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

Step 2.3.3

Divide $3$ by $0.5$ .

$f (1.5) = 6$

Step 2.4

The final answer is $6$ .

$6$

Step 3