Algebra Examples

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

Step 1

To divide by a fraction, multiply by its reciprocal.

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

Step 2

Cancel the common factor of $n + 3$ .

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Step 2.1

Factor $n + 3$ out of $(n - 1) (n + 3)$ .

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

Step 2.2

Cancel the common factor.

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

Step 2.3

Rewrite the expression.

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

Step 3

Multiply $\frac{1}{n + 2}$ by $\frac{{(n - 1)}^{2}}{n - 1}$ .

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

Step 4

Cancel the common factor of ${(n - 1)}^{2}$ and $n - 1$ .

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Step 4.1

Factor $n - 1$ out of ${(n - 1)}^{2}$ .

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

Step 4.2

Cancel the common factors.

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Step 4.2.1

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

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

Step 4.2.2

Cancel the common factor.

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

Step 4.2.3

Rewrite the expression.

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