Basic Math Examples

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

Step 1

Reduce the expression by cancelling the common factors.

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Step 1.1

Cancel the common factor of $z$ .

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Step 1.1.1

Cancel the common factor.

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

Step 1.1.2

Rewrite the expression.

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

Step 1.2

Divide $z - (\frac{z}{z - (\frac{z^{2}}{z + 1})})$ by $1$ .

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

Step 2

Simplify each term.

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Step 2.1

Simplify the denominator.

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Step 2.1.1

To write $z$ as a fraction with a common denominator, multiply by $\frac{z + 1}{z + 1}$ .

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

Step 2.1.2

Combine the numerators over the common denominator.

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

Step 2.1.3

Reorder terms.

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

Step 2.1.4

Rewrite $\frac{- z^{2} + z (z + 1)}{z + 1}$ in a factored form.

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Step 2.1.4.1

Factor $z$ out of $- z^{2} + z (z + 1)$ .

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Step 2.1.4.1.1

Factor $z$ out of $- z^{2}$ .

$z - \frac{z}{\frac{z (- z) + z (z + 1)}{z + 1}}$

Step 2.1.4.1.2

Factor $z$ out of $z (- z) + z (z + 1)$ .

$z - \frac{z}{\frac{z (- z + z + 1)}{z + 1}}$

Step 2.1.4.2

Add $- z$ and $z$ .

$z - \frac{z}{\frac{z (0 + 1)}{z + 1}}$

Step 2.1.4.3

Add $0$ and $1$ .

$z - \frac{z}{\frac{z \cdot 1}{z + 1}}$

Step 2.1.5

Multiply $z$ by $1$ .

$z - \frac{z}{\frac{z}{z + 1}}$

Step 2.2

Multiply the numerator by the reciprocal of the denominator.

$z - (z \frac{z + 1}{z})$

Step 2.3

Cancel the common factor of $z$ .

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Step 2.3.1

Cancel the common factor.

$z - (z \frac{z + 1}{z})$

Step 2.3.2

Rewrite the expression.

$z - (z + 1)$

Step 2.4

Apply the distributive property.

$z - z - 1 \cdot 1$

Step 2.5

Multiply $- 1$ by $1$ .

$z - z - 1$

Step 3

Simplify by adding terms.

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Step 3.1

Subtract $z$ from $z$ .

$0 - 1$

Step 3.2

Subtract $1$ from $0$ .

$- 1$