Finite Math Examples

$\frac{z - 6 + \frac{3}{z}}{z - 4 + \frac{2}{z}}$

Step 1

Multiply the numerator and denominator of the fraction by $z$ .

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Step 1.1

Multiply $\frac{z - 6 + \frac{3}{z}}{z - 4 + \frac{2}{z}}$ by $\frac{z}{z}$ .

$\frac{z}{z} \cdot \frac{z - 6 + \frac{3}{z}}{z - 4 + \frac{2}{z}}$

Step 1.2

Combine.

$\frac{z (z - 6 + \frac{3}{z})}{z (z - 4 + \frac{2}{z})}$

Step 2

Apply the distributive property.

$\frac{z \cdot z + z \cdot - 6 + z \frac{3}{z}}{z \cdot z + z \cdot - 4 + z \frac{2}{z}}$

Step 3

Simplify by cancelling.

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Step 3.1

Cancel the common factor of $z$ .

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Step 3.1.1

Cancel the common factor.

$\frac{z \cdot z + z \cdot - 6 + z \frac{3}{z}}{z \cdot z + z \cdot - 4 + z \frac{2}{z}}$

Step 3.1.2

Rewrite the expression.

$\frac{z \cdot z + z \cdot - 6 + 3}{z \cdot z + z \cdot - 4 + z \frac{2}{z}}$

Step 3.2

Cancel the common factor of $z$ .

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Step 3.2.1

Cancel the common factor.

$\frac{z \cdot z + z \cdot - 6 + 3}{z \cdot z + z \cdot - 4 + z \frac{2}{z}}$

Step 3.2.2

Rewrite the expression.

$\frac{z \cdot z + z \cdot - 6 + 3}{z \cdot z + z \cdot - 4 + 2}$

Step 4

Simplify the numerator.

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Step 4.1

Multiply $z$ by $z$ .

$\frac{z^{2} + z \cdot - 6 + 3}{z \cdot z + z \cdot - 4 + 2}$

Step 4.2

Move $- 6$ to the left of $z$ .

$\frac{z^{2} - 6 z + 3}{z \cdot z + z \cdot - 4 + 2}$

Step 5

Simplify the denominator.

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Step 5.1

Multiply $z$ by $z$ .

$\frac{z^{2} - 6 z + 3}{z^{2} + z \cdot - 4 + 2}$

Step 5.2

Move $- 4$ to the left of $z$ .

$\frac{z^{2} - 6 z + 3}{z^{2} - 4 z + 2}$