Simplify (x^2-3x)/(x-2)*(x^2+x-6)/x

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

Step 1

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

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

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

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

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

Factor $x$ out of $x \cdot x + x \cdot - 3$ .

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

Step 2

Factor $x^{2} + x - 6$ 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 $- 6$ and whose sum is $1$ .

$- 2, 3$

Write the factored form using these integers.

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

Step 3

Reduce the expression by cancelling the common factors.

Cancel the common factor of $x$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $x - 2$ .

Cancel the common factor.

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

Rewrite the expression.

$(x - 3) \cdot (x + 3)$

Step 4

Expand $(x - 3) (x + 3)$ using the FOIL Method.

Apply the distributive property.

$x (x + 3) - 3 (x + 3)$

Apply the distributive property.

$x \cdot x + x \cdot 3 - 3 (x + 3)$

Apply the distributive property.

$x \cdot x + x \cdot 3 - 3 x - 3 \cdot 3$

Step 5

Simplify terms.

Combine the opposite terms in $x \cdot x + x \cdot 3 - 3 x - 3 \cdot 3$ .

Reorder the factors in the terms $x \cdot 3$ and $- 3 x$ .

$x \cdot x + 3 x - 3 x - 3 \cdot 3$

Subtract $3 x$ from $3 x$ .

$x \cdot x + 0 - 3 \cdot 3$

Add $x \cdot x$ and $0$ .

$x \cdot x - 3 \cdot 3$

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} - 3 \cdot 3$

Multiply $- 3$ by $3$ .

$x^{2} - 9$

Simplify (x^2-3x)/(x-2)*(x^2+x-6)/x

Related Questions

Support LCMGCF.com by disabling your adblocker.