Simplify (2x^2-4x-6)/(3x^2-6x-9)

$\frac{2 x^{2} - 4 x - 6}{3 x^{2} - 6 x - 9}$

Step 1

Simplify the numerator.

Factor $2$ out of $2 x^{2} - 4 x - 6$ .

Factor $2$ out of $2 x^{2}$ .

$\frac{2 (x^{2}) - 4 x - 6}{3 x^{2} - 6 x - 9}$

Factor $2$ out of $- 4 x$ .

$\frac{2 (x^{2}) + 2 (- 2 x) - 6}{3 x^{2} - 6 x - 9}$

Factor $2$ out of $- 6$ .

$\frac{2 x^{2} + 2 (- 2 x) + 2 \cdot - 3}{3 x^{2} - 6 x - 9}$

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

$\frac{2 (x^{2} - 2 x) + 2 \cdot - 3}{3 x^{2} - 6 x - 9}$

Factor $2$ out of $2 (x^{2} - 2 x) + 2 \cdot - 3$ .

$\frac{2 (x^{2} - 2 x - 3)}{3 x^{2} - 6 x - 9}$

Factor $x^{2} - 2 x - 3$ 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 $- 3$ and whose sum is $- 2$ .

$- 3, 1$

Write the factored form using these integers.

$\frac{2 ((x - 3) (x + 1))}{3 x^{2} - 6 x - 9}$

$\frac{2 (x - 3) (x + 1)}{3 x^{2} - 6 x - 9}$

Step 2

Simplify the denominator.

Factor $3$ out of $3 x^{2} - 6 x - 9$ .

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

$\frac{2 (x - 3) (x + 1)}{3 (x^{2}) - 6 x - 9}$

Factor $3$ out of $- 6 x$ .

$\frac{2 (x - 3) (x + 1)}{3 (x^{2}) + 3 (- 2 x) - 9}$

Factor $3$ out of $- 9$ .

$\frac{2 (x - 3) (x + 1)}{3 x^{2} + 3 (- 2 x) + 3 \cdot - 3}$

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

$\frac{2 (x - 3) (x + 1)}{3 (x^{2} - 2 x) + 3 \cdot - 3}$

Factor $3$ out of $3 (x^{2} - 2 x) + 3 \cdot - 3$ .

$\frac{2 (x - 3) (x + 1)}{3 (x^{2} - 2 x - 3)}$

Factor $x^{2} - 2 x - 3$ 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 $- 3$ and whose sum is $- 2$ .

$- 3, 1$

Write the factored form using these integers.

$\frac{2 (x - 3) (x + 1)}{3 ((x - 3) (x + 1))}$

$\frac{2 (x - 3) (x + 1)}{3 (x - 3) (x + 1)}$

Step 3

Reduce the expression by cancelling the common factors.

Cancel the common factor of $x - 3$ .

Cancel the common factor.

$\frac{2 (x - 3) (x + 1)}{3 (x - 3) (x + 1)}$

Rewrite the expression.

$\frac{2 (x + 1)}{3 (x + 1)}$

Cancel the common factor of $x + 1$ .

Cancel the common factor.

$\frac{2 (x + 1)}{3 (x + 1)}$

Rewrite the expression.

$\frac{2}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{2}{3}$

Decimal Form:

$0.\overline{6}$

Simplify (2x^2-4x-6)/(3x^2-6x-9)

Related Questions

Support LCMGCF.com by disabling your adblocker.