Basic Math Examples

$\frac{z^{2} - 10 z + 21}{3 z} \cdot \frac{z + 2}{z - 3}$

Step 1

Factor $z^{2} - 10 z + 21$ 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 $21$ and whose sum is $- 10$ .

$- 7, - 3$

Step 1.2

Write the factored form using these integers.

$\frac{(z - 7) (z - 3)}{3 z} \cdot \frac{z + 2}{z - 3}$

Step 2

Simplify terms.

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Step 2.1

Cancel the common factor of $z - 3$ .

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Step 2.1.1

Factor $z - 3$ out of $(z - 7) (z - 3)$ .

$\frac{(z - 3) (z - 7)}{3 z} \cdot \frac{z + 2}{z - 3}$

Step 2.1.2

Cancel the common factor.

$\frac{(z - 3) (z - 7)}{3 z} \cdot \frac{z + 2}{z - 3}$

Step 2.1.3

Rewrite the expression.

$\frac{z - 7}{3 z} \cdot (z + 2)$

Step 2.2

Multiply $\frac{z - 7}{3 z}$ by $z + 2$ .

$\frac{(z - 7) (z + 2)}{3 z}$