Basic Math Examples

$\frac{n y}{n^{2} - 4 n} \cdot n^{2} - \frac{16}{4 y}$

Step 1

Simplify each term.

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Step 1.1

Factor $n$ out of $n^{2} - 4 n$ .

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Step 1.1.1

Factor $n$ out of $n^{2}$ .

$\frac{n y}{n \cdot n - 4 n} \cdot n^{2} - \frac{16}{4 y}$

Step 1.1.2

Factor $n$ out of $- 4 n$ .

$\frac{n y}{n \cdot n + n \cdot - 4} \cdot n^{2} - \frac{16}{4 y}$

Step 1.1.3

Factor $n$ out of $n \cdot n + n \cdot - 4$ .

$\frac{n y}{n (n - 4)} \cdot n^{2} - \frac{16}{4 y}$

Step 1.2

Cancel the common factor of $n$ .

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Step 1.2.1

Factor $n$ out of $n^{2}$ .

$\frac{n y}{n (n - 4)} \cdot (n \cdot n) - \frac{16}{4 y}$

Step 1.2.2

Cancel the common factor.

$\frac{n y}{n (n - 4)} \cdot (n \cdot n) - \frac{16}{4 y}$

Step 1.2.3

Rewrite the expression.

$\frac{n y}{n - 4} \cdot n - \frac{16}{4 y}$

Step 1.3

Combine $\frac{n y}{n - 4}$ and $n$ .

$\frac{n y n}{n - 4} - \frac{16}{4 y}$

Step 1.4

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

$\frac{n^{1} n y}{n - 4} - \frac{16}{4 y}$

Step 1.5

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

$\frac{n^{1} n^{1} y}{n - 4} - \frac{16}{4 y}$

Step 1.6

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

$\frac{n^{1 + 1} y}{n - 4} - \frac{16}{4 y}$

Step 1.7

Add $1$ and $1$ .

$\frac{n^{2} y}{n - 4} - \frac{16}{4 y}$

Step 1.8

Cancel the common factor of $16$ and $4$ .

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Step 1.8.1

Factor $4$ out of $16$ .

$\frac{n^{2} y}{n - 4} - \frac{4 \cdot 4}{4 y}$

Step 1.8.2

Cancel the common factors.

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Step 1.8.2.1

Factor $4$ out of $4 y$ .

$\frac{n^{2} y}{n - 4} - \frac{4 \cdot 4}{4 (y)}$

Step 1.8.2.2

Cancel the common factor.

$\frac{n^{2} y}{n - 4} - \frac{4 \cdot 4}{4 y}$

Step 1.8.2.3

Rewrite the expression.

$\frac{n^{2} y}{n - 4} - \frac{4}{y}$

Step 2

To write $\frac{n^{2} y}{n - 4}$ as a fraction with a common denominator, multiply by $\frac{y}{y}$ .

$\frac{n^{2} y}{n - 4} \cdot \frac{y}{y} - \frac{4}{y}$

Step 3

To write $- \frac{4}{y}$ as a fraction with a common denominator, multiply by $\frac{n - 4}{n - 4}$ .

$\frac{n^{2} y}{n - 4} \cdot \frac{y}{y} - \frac{4}{y} \cdot \frac{n - 4}{n - 4}$

Step 4

Write each expression with a common denominator of $(n - 4) y$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{n^{2} y}{n - 4}$ by $\frac{y}{y}$ .

$\frac{n^{2} y \cdot y}{(n - 4) y} - \frac{4}{y} \cdot \frac{n - 4}{n - 4}$

Step 4.2

Multiply $\frac{4}{y}$ by $\frac{n - 4}{n - 4}$ .

$\frac{n^{2} y \cdot y}{(n - 4) y} - \frac{4 (n - 4)}{y (n - 4)}$

Step 4.3

Reorder the factors of $(n - 4) y$ .

$\frac{n^{2} y \cdot y}{y (n - 4)} - \frac{4 (n - 4)}{y (n - 4)}$

Step 5

Combine the numerators over the common denominator.

$\frac{n^{2} y \cdot y - 4 (n - 4)}{y (n - 4)}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $y$ by $y$ by adding the exponents.

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Step 6.1.1

Move $y$ .

$\frac{n^{2} (y \cdot y) - 4 (n - 4)}{y (n - 4)}$

Step 6.1.2

Multiply $y$ by $y$ .

$\frac{n^{2} y^{2} - 4 (n - 4)}{y (n - 4)}$

Step 6.2

Apply the distributive property.

$\frac{n^{2} y^{2} - 4 n - 4 \cdot - 4}{y (n - 4)}$

Step 6.3

Multiply $- 4$ by $- 4$ .

$\frac{n^{2} y^{2} - 4 n + 16}{y (n - 4)}$