Simplify 4/(9x)-(3x)/7

$\frac{4}{9 x} - \frac{3 x}{7}$

Step 1

To write $\frac{4}{9 x}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{4}{9 x} \cdot \frac{7}{7} - \frac{3 x}{7}$

Step 2

To write $- \frac{3 x}{7}$ as a fraction with a common denominator, multiply by $\frac{9 x}{9 x}$ .

$\frac{4}{9 x} \cdot \frac{7}{7} - \frac{3 x}{7} \cdot \frac{9 x}{9 x}$

Step 3

Write each expression with a common denominator of $63 x$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{4}{9 x}$ by $\frac{7}{7}$ .

$\frac{4 \cdot 7}{9 x \cdot 7} - \frac{3 x}{7} \cdot \frac{9 x}{9 x}$

Multiply $7$ by $9$ .

$\frac{4 \cdot 7}{63 x} - \frac{3 x}{7} \cdot \frac{9 x}{9 x}$

Multiply $\frac{3 x}{7}$ by $\frac{9 x}{9 x}$ .

$\frac{4 \cdot 7}{63 x} - \frac{3 x (9 x)}{7 (9 x)}$

Multiply $9$ by $7$ .

$\frac{4 \cdot 7}{63 x} - \frac{3 x (9 x)}{63 x}$

Step 4

Combine the numerators over the common denominator.

$\frac{4 \cdot 7 - 3 x (9 x)}{63 x}$

Step 5

Simplify the numerator.

Multiply $4$ by $7$ .

$\frac{28 - 3 x (9 x)}{63 x}$

Rewrite using the commutative property of multiplication.

$\frac{28 - 3 \cdot 9 x \cdot x}{63 x}$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$\frac{28 - 3 \cdot 9 (x \cdot x)}{63 x}$

Multiply $x$ by $x$ .

$\frac{28 - 3 \cdot 9 x^{2}}{63 x}$

Multiply $- 3$ by $9$ .

$\frac{28 - 27 x^{2}}{63 x}$