Simplify (((a-4)(a+3))/(a^2-a))÷(a+3)*(a-1)/(a-4)

$\frac{(a - 4) (a + 3)}{a^{2} - a} \div (a + 3) \cdot \frac{a - 1}{a - 4}$

Step 1

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

Factor $a$ out of $a^{2}$ .

$\frac{(a - 4) (a + 3)}{a \cdot a - a} \div (a + 3) \cdot \frac{a - 1}{a - 4}$

Factor $a$ out of $- a$ .

$\frac{(a - 4) (a + 3)}{a \cdot a + a \cdot - 1} \div (a + 3) \cdot \frac{a - 1}{a - 4}$

Factor $a$ out of $a \cdot a + a \cdot - 1$ .

$\frac{(a - 4) (a + 3)}{a (a - 1)} \div (a + 3) \cdot \frac{a - 1}{a - 4}$

Step 2

Rewrite the division as a fraction.

$\frac{\frac{(a - 4) (a + 3)}{a (a - 1)}}{a + 3} \cdot \frac{a - 1}{a - 4}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$\frac{(a - 4) (a + 3)}{a (a - 1)} \cdot \frac{1}{a + 3} \cdot \frac{a - 1}{a - 4}$

Step 4

Cancel the common factor of $a + 3$ .

Factor $a + 3$ out of $(a - 4) (a + 3)$ .

$\frac{(a + 3) (a - 4)}{a (a - 1)} \cdot \frac{1}{a + 3} \cdot \frac{a - 1}{a - 4}$

Cancel the common factor.

$\frac{(a + 3) (a - 4)}{a (a - 1)} \cdot \frac{1}{a + 3} \cdot \frac{a - 1}{a - 4}$

Rewrite the expression.

$\frac{a - 4}{a (a - 1)} \cdot \frac{a - 1}{a - 4}$

Step 5

Cancel the common factor of $a - 4$ .

Cancel the common factor.

$\frac{a - 4}{a (a - 1)} \cdot \frac{a - 1}{a - 4}$

Rewrite the expression.

$\frac{1}{a (a - 1)} \cdot (a - 1)$

Step 6

Cancel the common factor of $a - 1$ .

Factor $a - 1$ out of $a (a - 1)$ .

$\frac{1}{(a - 1) a} \cdot (a - 1)$

Cancel the common factor.

$\frac{1}{(a - 1) a} \cdot (a - 1)$

Rewrite the expression.

$\frac{1}{a}$