Simplify (20a^2-100a)/(a-1)*1/(16a^3-80a^2)

$\frac{20 a^{2} - 100 a}{a - 1} \cdot \frac{1}{16 a^{3} - 80 a^{2}}$

Step 1

Factor $20 a$ out of $20 a^{2} - 100 a$ .

Factor $20 a$ out of $20 a^{2}$ .

$\frac{20 a (a) - 100 a}{a - 1} \cdot \frac{1}{16 a^{3} - 80 a^{2}}$

Factor $20 a$ out of $- 100 a$ .

$\frac{20 a (a) + 20 a (- 5)}{a - 1} \cdot \frac{1}{16 a^{3} - 80 a^{2}}$

Factor $20 a$ out of $20 a (a) + 20 a (- 5)$ .

$\frac{20 a (a - 5)}{a - 1} \cdot \frac{1}{16 a^{3} - 80 a^{2}}$

Step 2

Factor $16 a^{2}$ out of $16 a^{3} - 80 a^{2}$ .

Factor $16 a^{2}$ out of $16 a^{3}$ .

$\frac{20 a (a - 5)}{a - 1} \cdot \frac{1}{16 a^{2} (a) - 80 a^{2}}$

Factor $16 a^{2}$ out of $- 80 a^{2}$ .

$\frac{20 a (a - 5)}{a - 1} \cdot \frac{1}{16 a^{2} (a) + 16 a^{2} (- 5)}$

Factor $16 a^{2}$ out of $16 a^{2} (a) + 16 a^{2} (- 5)$ .

$\frac{20 a (a - 5)}{a - 1} \cdot \frac{1}{16 a^{2} (a - 5)}$

Step 3

Cancel the common factor of $4 a (a - 5)$ .

Factor $4 a (a - 5)$ out of $20 a (a - 5)$ .

$\frac{4 a (a - 5) (5)}{a - 1} \cdot \frac{1}{16 a^{2} (a - 5)}$

Factor $4 a (a - 5)$ out of $16 a^{2} (a - 5)$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{5}{a - 1} \cdot \frac{1}{4 a}$

Step 4

Multiply $\frac{5}{a - 1}$ by $\frac{1}{4 a}$ .

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

Step 5

Simplify the expression.

Move $4$ to the left of $a - 1$ .

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

Reorder factors in $\frac{5}{4 (a - 1) a}$ .

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