Pre-Algebra Examples

$\frac{4 x y}{1 + \frac{4}{x y}}$

Step 1

Simplify the denominator.

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Step 1.1

Write $1$ as a fraction with a common denominator.

$\frac{4 x y}{\frac{x y}{x y} + \frac{4}{x y}}$

Step 1.2

Combine the numerators over the common denominator.

$\frac{4 x y}{\frac{x y + 4}{x y}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$4 x y \frac{x y}{x y + 4}$

Step 3

Multiply $4 x y \frac{x y}{x y + 4}$ .

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Step 3.1

Combine $4$ and $\frac{x y}{x y + 4}$ .

$x y \frac{4 (x y)}{x y + 4}$

Step 3.2

Combine $x$ and $\frac{4 (x y)}{x y + 4}$ .

$y \frac{x (4 (x y))}{x y + 4}$

Step 3.3

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

$y \frac{4 (x^{1} x y)}{x y + 4}$

Step 3.4

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

$y \frac{4 (x^{1} x^{1} y)}{x y + 4}$

Step 3.5

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

$y \frac{4 (x^{1 + 1} y)}{x y + 4}$

Step 3.6

Add $1$ and $1$ .

$y \frac{4 (x^{2} y)}{x y + 4}$

Step 3.7

Combine $y$ and $\frac{4 (x^{2} y)}{x y + 4}$ .

$\frac{y (4 (x^{2} y))}{x y + 4}$

Step 3.8

Raise $y$ to the power of $1$ .

$\frac{4 (x^{2} (y^{1} y))}{x y + 4}$

Step 3.9

Raise $y$ to the power of $1$ .

$\frac{4 (x^{2} (y^{1} y^{1}))}{x y + 4}$

Step 3.10

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

$\frac{4 (x^{2} y^{1 + 1})}{x y + 4}$

Step 3.11

Add $1$ and $1$ .

$\frac{4 (x^{2} y^{2})}{x y + 4}$

$\frac{4 x^{2} y^{2}}{x y + 4}$