Algebra Examples

$\frac{- 7 n^{2}}{- 14 n^{2} - 35 n}$

Step 1

Factor $7 n$ out of $- 14 n^{2} - 35 n$ .

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Step 1.1

Factor $7 n$ out of $- 14 n^{2}$ .

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

Step 1.2

Factor $7 n$ out of $- 35 n$ .

$\frac{- 7 n^{2}}{7 n (- 2 n) + 7 n (- 5)}$

Step 1.3

Factor $7 n$ out of $7 n (- 2 n) + 7 n (- 5)$ .

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

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

Step 2

Cancel the common factor of $- 7$ and $7$ .

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Step 2.1

Factor $7$ out of $- 7 n^{2}$ .

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

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $7$ out of $7 n (- 2 n - 5)$ .

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

Step 2.2.2

Cancel the common factor.

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

Step 2.2.3

Rewrite the expression.

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

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

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

Step 3

Cancel the common factor of $n^{2}$ and $n$ .

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Step 3.1

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

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

Step 3.2

Cancel the common factors.

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Step 3.2.1

Cancel the common factor.

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

Step 3.2.2

Rewrite the expression.

$\frac{- n}{- 2 n - 5}$

$\frac{- n}{- 2 n - 5}$

$\frac{- n}{- 2 n - 5}$

Step 4

Move the negative in front of the fraction.

$- \frac{n}{- 2 n - 5}$

Step 5

Factor $- 1$ out of $- 2 n$ .

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

Step 6

Rewrite $- 5$ as $- 1 (5)$ .

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

Step 7

Factor $- 1$ out of $- (2 n) - 1 (5)$ .

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

Step 8

Simplify the expression.

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Step 8.1

Rewrite $- (2 n + 5)$ as $- 1 (2 n + 5)$ .

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

Step 8.2

Move the negative in front of the fraction.

$- - \frac{n}{2 n + 5}$

Step 8.3

Multiply $- 1$ by $- 1$ .

$1 \frac{n}{2 n + 5}$

Step 8.4

Multiply $\frac{n}{2 n + 5}$ by $1$ .

$\frac{n}{2 n + 5}$

$\frac{n}{2 n + 5}$

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