Simplify (15a^2bn-45a^2bm)/(10a^2b^2n-30a^2b^2m)

$\frac{15 a^{2} b n - 45 a^{2} b m}{10 a^{2} b^{2} n - 30 a^{2} b^{2} m}$

Step 1

Factor $15 a^{2} b$ out of $15 a^{2} b n - 45 a^{2} b m$ .

Factor $15 a^{2} b$ out of $15 a^{2} b n$ .

$\frac{15 a^{2} b (n) - 45 a^{2} b m}{10 a^{2} b^{2} n - 30 a^{2} b^{2} m}$

Factor $15 a^{2} b$ out of $- 45 a^{2} b m$ .

$\frac{15 a^{2} b (n) + 15 a^{2} b (- 3 m)}{10 a^{2} b^{2} n - 30 a^{2} b^{2} m}$

Factor $15 a^{2} b$ out of $15 a^{2} b (n) + 15 a^{2} b (- 3 m)$ .

$\frac{15 a^{2} b (n - 3 m)}{10 a^{2} b^{2} n - 30 a^{2} b^{2} m}$

Step 2

Factor $10 a^{2} b^{2}$ out of $10 a^{2} b^{2} n - 30 a^{2} b^{2} m$ .

Factor $10 a^{2} b^{2}$ out of $10 a^{2} b^{2} n$ .

$\frac{15 a^{2} b (n - 3 m)}{10 a^{2} b^{2} (n) - 30 a^{2} b^{2} m}$

Factor $10 a^{2} b^{2}$ out of $- 30 a^{2} b^{2} m$ .

$\frac{15 a^{2} b (n - 3 m)}{10 a^{2} b^{2} (n) + 10 a^{2} b^{2} (- 3 m)}$

Factor $10 a^{2} b^{2}$ out of $10 a^{2} b^{2} (n) + 10 a^{2} b^{2} (- 3 m)$ .

$\frac{15 a^{2} b (n - 3 m)}{10 a^{2} b^{2} (n - 3 m)}$

Step 3

Cancel the common factor of $15$ and $10$ .

Factor $5$ out of $15 a^{2} b (n - 3 m)$ .

$\frac{5 (3 a^{2} b (n - 3 m))}{10 a^{2} b^{2} (n - 3 m)}$

Cancel the common factors.

Factor $5$ out of $10 a^{2} b^{2} (n - 3 m)$ .

$\frac{5 (3 a^{2} b (n - 3 m))}{5 (2 a^{2} b^{2} (n - 3 m))}$

Cancel the common factor.

$\frac{5 (3 a^{2} b (n - 3 m))}{5 (2 a^{2} b^{2} (n - 3 m))}$

Rewrite the expression.

$\frac{3 a^{2} b (n - 3 m)}{2 a^{2} b^{2} (n - 3 m)}$

Step 4

Cancel the common factor of $a^{2}$ .

Cancel the common factor.

$\frac{3 a^{2} b (n - 3 m)}{2 a^{2} b^{2} (n - 3 m)}$

Rewrite the expression.

$\frac{3 b (n - 3 m)}{2 b^{2} (n - 3 m)}$

Step 5

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

Factor $b$ out of $3 b (n - 3 m)$ .

$\frac{b (3 (n - 3 m))}{2 b^{2} (n - 3 m)}$

Cancel the common factors.

Factor $b$ out of $2 b^{2} (n - 3 m)$ .

$\frac{b (3 (n - 3 m))}{b (2 b (n - 3 m))}$

Cancel the common factor.

$\frac{b (3 (n - 3 m))}{b (2 b (n - 3 m))}$

Rewrite the expression.

$\frac{3 (n - 3 m)}{2 b (n - 3 m)}$

Step 6

Cancel the common factor of $n - 3 m$ .

Cancel the common factor.

$\frac{3 (n - 3 m)}{2 b (n - 3 m)}$

Rewrite the expression.

$\frac{3}{2 b}$

Simplify (15a^2bn-45a^2bm)/(10a^2b^2n-30a^2b^2m)

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