Simplify (3d^2-3d)/(3d-6)-6/(3d-6)

$\frac{3 d^{2} - 3 d}{3 d - 6} - \frac{6}{3 d - 6}$

Step 1

Simplify terms.

Combine the numerators over the common denominator.

$\frac{3 d^{2} - 3 d - 6}{3 d - 6}$

Cancel the common factor of $3 d^{2} - 3 d - 6$ and $3 d - 6$ .

Factor $3$ out of $3 d^{2}$ .

$\frac{3 (d^{2}) - 3 d - 6}{3 d - 6}$

Factor $3$ out of $- 3 d$ .

$\frac{3 (d^{2}) + 3 (- d) - 6}{3 d - 6}$

Factor $3$ out of $3 (d^{2}) + 3 (- d)$ .

$\frac{3 (d^{2} - d) - 6}{3 d - 6}$

Factor $3$ out of $- 6$ .

$\frac{3 (d^{2} - d) + 3 \cdot - 2}{3 d - 6}$

Factor $3$ out of $3 (d^{2} - d) + 3 (- 2)$ .

$\frac{3 (d^{2} - d - 2)}{3 d - 6}$

Cancel the common factors.

Factor $3$ out of $3 d$ .

$\frac{3 (d^{2} - d - 2)}{3 (d) - 6}$

Factor $3$ out of $- 6$ .

$\frac{3 (d^{2} - d - 2)}{3 d + 3 \cdot - 2}$

Factor $3$ out of $3 d + 3 \cdot - 2$ .

$\frac{3 (d^{2} - d - 2)}{3 (d - 2)}$

Cancel the common factor.

$\frac{3 (d^{2} - d - 2)}{3 (d - 2)}$

Rewrite the expression.

$\frac{d^{2} - d - 2}{d - 2}$

Step 2

Factor $d^{2} - d - 2$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 2$ and whose sum is $- 1$ .

$- 2, 1$

Write the factored form using these integers.

$\frac{(d - 2) (d + 1)}{d - 2}$

Step 3

Cancel the common factor of $d - 2$ .

Cancel the common factor.

$\frac{(d - 2) (d + 1)}{d - 2}$

Divide $d + 1$ by $1$ .

$d + 1$

Simplify (3d^2-3d)/(3d-6)-6/(3d-6)

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