Algebra Examples

$\frac{n + 6}{27 n^{2} - 54 n} - \frac{n - 3}{27 n^{2} - 54 n}$

Step 1

Combine the numerators over the common denominator.

$\frac{n + 6 - (n - 3)}{27 n^{2} - 54 n}$

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

$\frac{n + 6 - n - - 3}{27 n^{2} - 54 n}$

Step 2.2

Multiply $- 1$ by $- 3$ .

$\frac{n + 6 - n + 3}{27 n^{2} - 54 n}$

$\frac{n + 6 - n + 3}{27 n^{2} - 54 n}$

Step 3

Simplify terms.

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Step 3.1

Combine the opposite terms in $n + 6 - n + 3$ .

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Step 3.1.1

Subtract $n$ from $n$ .

$\frac{0 + 6 + 3}{27 n^{2} - 54 n}$

Step 3.1.2

Add $0$ and $6$ .

$\frac{6 + 3}{27 n^{2} - 54 n}$

$\frac{6 + 3}{27 n^{2} - 54 n}$

Step 3.2

Add $6$ and $3$ .

$\frac{9}{27 n^{2} - 54 n}$

Step 3.3

Factor $27 n$ out of $27 n^{2} - 54 n$ .

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Step 3.3.1

Factor $27 n$ out of $27 n^{2}$ .

$\frac{9}{27 n (n) - 54 n}$

Step 3.3.2

Factor $27 n$ out of $- 54 n$ .

$\frac{9}{27 n (n) + 27 n (- 2)}$

Step 3.3.3

Factor $27 n$ out of $27 n (n) + 27 n (- 2)$ .

$\frac{9}{27 n (n - 2)}$

$\frac{9}{27 n (n - 2)}$

Step 3.4

Cancel the common factor of $9$ and $27$ .

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Step 3.4.1

Factor $9$ out of $9$ .

$\frac{9 (1)}{27 n (n - 2)}$

Step 3.4.2

Cancel the common factors.

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Step 3.4.2.1

Factor $9$ out of $27 n (n - 2)$ .

$\frac{9 (1)}{9 (3 n (n - 2))}$

Step 3.4.2.2

Cancel the common factor.

$\frac{9 \cdot 1}{9 (3 n (n - 2))}$

Step 3.4.2.3

Rewrite the expression.

$\frac{1}{3 n (n - 2)}$

$\frac{1}{3 n (n - 2)}$

$\frac{1}{3 n (n - 2)}$

$\frac{1}{3 n (n - 2)}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$