Simplify (4a)/(3bc)-(15b)/(5ac)

$\frac{4 a}{3 b c} - \frac{15 b}{5 a c}$

Step 1

Cancel the common factor of $15$ and $5$ .

Factor $5$ out of $15 b$ .

$\frac{4 a}{3 b c} - \frac{5 (3 b)}{5 a c}$

Cancel the common factors.

Factor $5$ out of $5 a c$ .

$\frac{4 a}{3 b c} - \frac{5 (3 b)}{5 (a c)}$

Cancel the common factor.

$\frac{4 a}{3 b c} - \frac{5 (3 b)}{5 (a c)}$

Rewrite the expression.

$\frac{4 a}{3 b c} - \frac{3 b}{a c}$

Step 2

To write $\frac{4 a}{3 b c}$ as a fraction with a common denominator, multiply by $\frac{a}{a}$ .

$\frac{4 a}{3 b c} \cdot \frac{a}{a} - \frac{3 b}{a c}$

Step 3

To write $- \frac{3 b}{a c}$ as a fraction with a common denominator, multiply by $\frac{3 b}{3 b}$ .

$\frac{4 a}{3 b c} \cdot \frac{a}{a} - \frac{3 b}{a c} \cdot \frac{3 b}{3 b}$

Step 4

Write each expression with a common denominator of $3 b c a$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{4 a}{3 b c}$ by $\frac{a}{a}$ .

$\frac{4 a \cdot a}{3 b c a} - \frac{3 b}{a c} \cdot \frac{3 b}{3 b}$

Multiply $\frac{3 b}{a c}$ by $\frac{3 b}{3 b}$ .

$\frac{4 a \cdot a}{3 b c a} - \frac{3 b (3 b)}{a c (3 b)}$

Reorder the factors of $3 b c a$ .

$\frac{4 a \cdot a}{3 a b c} - \frac{3 b (3 b)}{a c (3 b)}$

Reorder the factors of $a c (3 b)$ .

$\frac{4 a \cdot a}{3 a b c} - \frac{3 b (3 b)}{3 a b c}$

Step 5

Combine the numerators over the common denominator.

$\frac{4 a \cdot a - 3 b (3 b)}{3 a b c}$

Step 6

Simplify the numerator.

Raise $a$ to the power of $1$ .

$\frac{4 (a^{1} a) - 3 b (3 b)}{3 a b c}$

Raise $a$ to the power of $1$ .

$\frac{4 (a^{1} a^{1}) - 3 b (3 b)}{3 a b c}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{4 a^{1 + 1} - 3 b (3 b)}{3 a b c}$

Add $1$ and $1$ .

$\frac{4 a^{2} - 3 b (3 b)}{3 a b c}$

Rewrite $4 a^{2}$ as ${(2 a)}^{2}$ .

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

Rewrite $3 b (3 b)$ as ${(3 b)}^{2}$ .

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

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 2 a$ and $b = 3 b$ .

$\frac{(2 a + 3 b) (2 a - (3 b))}{3 a b c}$

Multiply $3$ by $- 1$ .

$\frac{(2 a + 3 b) (2 a - 3 b)}{3 a b c}$

Simplify (4a)/(3bc)-(15b)/(5ac)

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