Simplify ((2x+10)(x^2+x-6))/(4x^2+12x-40)

$\frac{(2 x + 10) (x^{2} + x - 6)}{4 x^{2} + 12 x - 40}$

Step 1

Cancel the common factor of $2 x + 10$ and $4 x^{2} + 12 x - 40$ .

Factor $2$ out of $(2 x + 10) (x^{2} + x - 6)$ .

$\frac{2 ((x + 5) (x^{2} + x - 6))}{4 x^{2} + 12 x - 40}$

Cancel the common factors.

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

$\frac{2 ((x + 5) (x^{2} + x - 6))}{2 (2 x^{2}) + 12 x - 40}$

Factor $2$ out of $12 x$ .

$\frac{2 ((x + 5) (x^{2} + x - 6))}{2 (2 x^{2}) + 2 (6 x) - 40}$

Factor $2$ out of $2 (2 x^{2}) + 2 (6 x)$ .

$\frac{2 ((x + 5) (x^{2} + x - 6))}{2 (2 x^{2} + 6 x) - 40}$

Factor $2$ out of $- 40$ .

$\frac{2 ((x + 5) (x^{2} + x - 6))}{2 (2 x^{2} + 6 x) + 2 (- 20)}$

Factor $2$ out of $2 (2 x^{2} + 6 x) + 2 (- 20)$ .

$\frac{2 ((x + 5) (x^{2} + x - 6))}{2 (2 x^{2} + 6 x - 20)}$

Cancel the common factor.

$\frac{2 ((x + 5) (x^{2} + x - 6))}{2 (2 x^{2} + 6 x - 20)}$

Rewrite the expression.

$\frac{(x + 5) (x^{2} + x - 6)}{2 x^{2} + 6 x - 20}$

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.

$\frac{(x + 5) ((x - 2) (x + 3))}{2 x^{2} + 6 x - 20}$

$\frac{(x + 5) (x - 2) (x + 3)}{2 x^{2} + 6 x - 20}$

Step 3

Simplify the denominator.

Factor $2$ out of $2 x^{2} + 6 x - 20$ .

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

$\frac{(x + 5) (x - 2) (x + 3)}{2 (x^{2}) + 6 x - 20}$

Factor $2$ out of $6 x$ .

$\frac{(x + 5) (x - 2) (x + 3)}{2 (x^{2}) + 2 (3 x) - 20}$

Factor $2$ out of $- 20$ .

$\frac{(x + 5) (x - 2) (x + 3)}{2 x^{2} + 2 (3 x) + 2 \cdot - 10}$

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

$\frac{(x + 5) (x - 2) (x + 3)}{2 (x^{2} + 3 x) + 2 \cdot - 10}$

Factor $2$ out of $2 (x^{2} + 3 x) + 2 \cdot - 10$ .

$\frac{(x + 5) (x - 2) (x + 3)}{2 (x^{2} + 3 x - 10)}$

Factor $x^{2} + 3 x - 10$ 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 $- 10$ and whose sum is $3$ .

$- 2, 5$

Write the factored form using these integers.

$\frac{(x + 5) (x - 2) (x + 3)}{2 ((x - 2) (x + 5))}$

$\frac{(x + 5) (x - 2) (x + 3)}{2 (x - 2) (x + 5)}$

Step 4

Reduce the expression by cancelling the common factors.

Cancel the common factor of $x + 5$ .

Cancel the common factor.

$\frac{(x + 5) (x - 2) (x + 3)}{2 (x - 2) (x + 5)}$

Rewrite the expression.

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

Cancel the common factor of $x - 2$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{x + 3}{2}$

Simplify ((2x+10)(x^2+x-6))/(4x^2+12x-40)

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