Basic Math Examples

$\frac{z^{2} - 3 z + 2}{z^{2} + 3 z - 2} \div \frac{z - 2}{3 z + 6}$

Step 1

To divide by a fraction, multiply by its reciprocal.

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

Step 2

Factor $z^{2} - 3 z + 2$ 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.

$\frac{(z - 2) (z - 1)}{z^{2} + 3 z - 2} \cdot \frac{3 z + 6}{z - 2}$

Step 3

Simplify terms.

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Step 3.1

Cancel the common factor of $z - 2$ .

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Step 3.1.1

Cancel the common factor.

$\frac{(z - 2) (z - 1)}{z^{2} + 3 z - 2} \cdot \frac{3 z + 6}{z - 2}$

Step 3.1.2

Rewrite the expression.

$\frac{z - 1}{z^{2} + 3 z - 2} (3 z + 6)$

Step 3.2

Multiply $\frac{z - 1}{z^{2} + 3 z - 2}$ by $3 z + 6$ .

$\frac{(z - 1) (3 z + 6)}{z^{2} + 3 z - 2}$

Step 4

Factor $3$ out of $3 z + 6$ .

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Step 4.1

Factor $3$ out of $3 z$ .

$\frac{(z - 1) (3 (z) + 6)}{z^{2} + 3 z - 2}$

Step 4.2

Factor $3$ out of $6$ .

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

Step 4.3

Factor $3$ out of $3 z + 3 \cdot 2$ .

$\frac{(z - 1) (3 (z + 2))}{z^{2} + 3 z - 2}$

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

Step 5

Move $3$ to the left of $z - 1$ .

$\frac{3 (z - 1) (z + 2)}{z^{2} + 3 z - 2}$