Algebra Examples

$\frac{35 n - 7}{5 n^{2} - n} - \frac{15 n - 3}{5 n^{2} - n}$

Step 1

Combine the numerators over the common denominator.

$\frac{35 n - 7 - (15 n - 3)}{5 n^{2} - n}$

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

$\frac{35 n - 7 - (15 n) - - 3}{5 n^{2} - n}$

Step 2.2

Multiply $15$ by $- 1$ .

$\frac{35 n - 7 - 15 n - - 3}{5 n^{2} - n}$

Step 2.3

Multiply $- 1$ by $- 3$ .

$\frac{35 n - 7 - 15 n + 3}{5 n^{2} - n}$

$\frac{35 n - 7 - 15 n + 3}{5 n^{2} - n}$

Step 3

Simplify terms.

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Step 3.1

Subtract $15 n$ from $35 n$ .

$\frac{20 n - 7 + 3}{5 n^{2} - n}$

Step 3.2

Add $- 7$ and $3$ .

$\frac{20 n - 4}{5 n^{2} - n}$

Step 3.3

Factor $4$ out of $20 n - 4$ .

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Step 3.3.1

Factor $4$ out of $20 n$ .

$\frac{4 (5 n) - 4}{5 n^{2} - n}$

Step 3.3.2

Factor $4$ out of $- 4$ .

$\frac{4 (5 n) + 4 (- 1)}{5 n^{2} - n}$

Step 3.3.3

Factor $4$ out of $4 (5 n) + 4 (- 1)$ .

$\frac{4 (5 n - 1)}{5 n^{2} - n}$

$\frac{4 (5 n - 1)}{5 n^{2} - n}$

Step 3.4

Factor $n$ out of $5 n^{2} - n$ .

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Step 3.4.1

Factor $n$ out of $5 n^{2}$ .

$\frac{4 (5 n - 1)}{n (5 n) - n}$

Step 3.4.2

Factor $n$ out of $- n$ .

$\frac{4 (5 n - 1)}{n (5 n) + n \cdot - 1}$

Step 3.4.3

Factor $n$ out of $n (5 n) + n \cdot - 1$ .

$\frac{4 (5 n - 1)}{n (5 n - 1)}$

$\frac{4 (5 n - 1)}{n (5 n - 1)}$

Step 3.5

Cancel the common factor of $5 n - 1$ .

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Step 3.5.1

Cancel the common factor.

$\frac{4 (5 n - 1)}{n (5 n - 1)}$

Step 3.5.2

Rewrite the expression.

$\frac{4}{n}$

$\frac{4}{n}$

$\frac{4}{n}$

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