Simplify ((n+3)/(n+2))÷(((n-1)(n+3))/((n-1)^2))

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

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 $n + 3$ .

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

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

Cancel the common factor.

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

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 $n - 1$ .

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

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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