Basic Math Examples

$\frac{x^{2} + x z + x y + y z}{y + z} \div \frac{x + y}{x + z}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{x^{2} + x z + x y + y z}{y + z} \cdot \frac{x + z}{x + y}$

Step 2

Simplify the numerator.

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Step 2.1

Factor out the greatest common factor from each group.

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Step 2.1.1

Group the first two terms and the last two terms.

$\frac{(x^{2} + x z) + x y + y z}{y + z} \cdot \frac{x + z}{x + y}$

Step 2.1.2

Factor out the greatest common factor (GCF) from each group.

$\frac{x (x + z) + y (x + z)}{y + z} \cdot \frac{x + z}{x + y}$

Step 2.2

Factor the polynomial by factoring out the greatest common factor, $x + z$ .

$\frac{(x + z) (x + y)}{y + z} \cdot \frac{x + z}{x + y}$

Step 3

Simplify terms.

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Step 3.1

Cancel the common factor of $x + y$ .

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Step 3.1.1

Factor $x + y$ out of $(x + z) (x + y)$ .

$\frac{(x + y) (x + z)}{y + z} \cdot \frac{x + z}{x + y}$

Step 3.1.2

Cancel the common factor.

$\frac{(x + y) (x + z)}{y + z} \cdot \frac{x + z}{x + y}$

Step 3.1.3

Rewrite the expression.

$\frac{x + z}{y + z} (x + z)$

Step 3.2

Multiply $\frac{x + z}{y + z}$ by $x + z$ .

$\frac{(x + z) (x + z)}{y + z}$

Step 4

Simplify the numerator.

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Step 4.1

Raise $x + z$ to the power of $1$ .

$\frac{{(x + z)}^{1} (x + z)}{y + z}$

Step 4.2

Raise $x + z$ to the power of $1$ .

$\frac{{(x + z)}^{1} {(x + z)}^{1}}{y + z}$

Step 4.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{{(x + z)}^{1 + 1}}{y + z}$

Step 4.4

Add $1$ and $1$ .

$\frac{{(x + z)}^{2}}{y + z}$