Finite Math Examples

$\frac{x^{2} + 3 x - 10}{x^{2} - 3 x + 2} \cdot \frac{x^{2} + x - 2}{x^{2} + 2 x - 15}$

Step 1

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

$- 2, 5$

Step 1.2

Write the factored form using these integers.

$\frac{(x - 2) (x + 5)}{x^{2} - 3 x + 2} \cdot \frac{x^{2} + x - 2}{x^{2} + 2 x - 15}$

Step 2

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

$- 2, - 1$

Step 2.2

Write the factored form using these integers.

$\frac{(x - 2) (x + 5)}{(x - 2) (x - 1)} \cdot \frac{x^{2} + x - 2}{x^{2} + 2 x - 15}$

Step 3

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

$- 1, 2$

Step 3.2

Write the factored form using these integers.

$\frac{(x - 2) (x + 5)}{(x - 2) (x - 1)} \cdot \frac{(x - 1) (x + 2)}{x^{2} + 2 x - 15}$

Step 4

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

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Step 4.1

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 $2$ .

$- 3, 5$

Step 4.2

Write the factored form using these integers.

$\frac{(x - 2) (x + 5)}{(x - 2) (x - 1)} \cdot \frac{(x - 1) (x + 2)}{(x - 3) (x + 5)}$

Step 5

Simplify terms.

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Step 5.1

Cancel the common factor of $x + 5$ .

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Step 5.1.1

Factor $x + 5$ out of $(x - 2) (x + 5)$ .

$\frac{(x + 5) (x - 2)}{(x - 2) (x - 1)} \cdot \frac{(x - 1) (x + 2)}{(x - 3) (x + 5)}$

Step 5.1.2

Factor $x + 5$ out of $(x - 3) (x + 5)$ .

$\frac{(x + 5) (x - 2)}{(x - 2) (x - 1)} \cdot \frac{(x - 1) (x + 2)}{(x + 5) (x - 3)}$

Step 5.1.3

Cancel the common factor.

$\frac{(x + 5) (x - 2)}{(x - 2) (x - 1)} \cdot \frac{(x - 1) (x + 2)}{(x + 5) (x - 3)}$

Step 5.1.4

Rewrite the expression.

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

Step 5.2

Cancel the common factor of $x - 1$ .

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Step 5.2.1

Factor $x - 1$ out of $(x - 2) (x - 1)$ .

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

Step 5.2.2

Cancel the common factor.

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

Step 5.2.3

Rewrite the expression.

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

Step 5.3

Multiply $\frac{x - 2}{x - 2}$ by $\frac{x + 2}{x - 3}$ .

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

Step 5.4

Cancel the common factor of $x - 2$ .

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Step 5.4.1

Cancel the common factor.

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

Step 5.4.2

Rewrite the expression.

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