Algebra Examples

$\frac{x^{2} - 3 x - 4}{x^{2} + 4 x + 3} \cdot \frac{x^{2} + 8 x + 15}{x - 4}$

Step 1

Factor $x^{2} - 3 x - 4$ using the AC method.

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Step 1.1

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 $- 4$ and whose sum is $- 3$ .

$- 4, 1$

Step 1.2

Write the factored form using these integers.

$\frac{(x - 4) (x + 1)}{x^{2} + 4 x + 3} \cdot \frac{x^{2} + 8 x + 15}{x - 4}$

Step 2

Factor $x^{2} + 4 x + 3$ using the AC method.

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Step 2.1

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 $4$ .

$1, 3$

Step 2.2

Write the factored form using these integers.

$\frac{(x - 4) (x + 1)}{(x + 1) (x + 3)} \cdot \frac{x^{2} + 8 x + 15}{x - 4}$

Step 3

Factor $x^{2} + 8 x + 15$ using the AC method.

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Step 3.1

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 $15$ and whose sum is $8$ .

$3, 5$

Step 3.2

Write the factored form using these integers.

$\frac{(x - 4) (x + 1)}{(x + 1) (x + 3)} \cdot \frac{(x + 3) (x + 5)}{x - 4}$

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

Cancel the common factor of $x - 4$ .

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Step 4.1.1

Cancel the common factor.

$\frac{(x - 4) (x + 1)}{(x + 1) (x + 3)} \cdot \frac{(x + 3) (x + 5)}{x - 4}$

Step 4.1.2

Rewrite the expression.

$\frac{x + 1}{(x + 1) (x + 3)} \cdot ((x + 3) (x + 5))$

Step 4.2

Cancel the common factor of $x + 3$ .

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Step 4.2.1

Factor $x + 3$ out of $(x + 1) (x + 3)$ .

$\frac{x + 1}{(x + 3) (x + 1)} \cdot ((x + 3) (x + 5))$

Step 4.2.2

Cancel the common factor.

$\frac{x + 1}{(x + 3) (x + 1)} \cdot ((x + 3) (x + 5))$

Step 4.2.3

Rewrite the expression.

$\frac{x + 1}{x + 1} \cdot (x + 5)$

Step 4.3

Cancel the common factor of $x + 1$ .

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Step 4.3.1

Cancel the common factor.

$\frac{x + 1}{x + 1} \cdot (x + 5)$

Step 4.3.2

Rewrite the expression.

$1 \cdot (x + 5)$

Step 4.4

Multiply $x + 5$ by $1$ .

$x + 5$