Simplify 7/(16x^3)-3/(8x^2)

$\frac{7}{16 x^{3}} - \frac{3}{8 x^{2}}$

Step 1

To write $- \frac{3}{8 x^{2}}$ as a fraction with a common denominator, multiply by $\frac{2 x}{2 x}$ .

$\frac{7}{16 x^{3}} - \frac{3}{8 x^{2}} \cdot \frac{2 x}{2 x}$

Step 2

Write each expression with a common denominator of $16 x^{3}$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{3}{8 x^{2}}$ by $\frac{2 x}{2 x}$ .

$\frac{7}{16 x^{3}} - \frac{3 (2 x)}{8 x^{2} (2 x)}$

Multiply $2$ by $8$ .

$\frac{7}{16 x^{3}} - \frac{3 (2 x)}{16 x^{2} x}$

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

$\frac{7}{16 x^{3}} - \frac{3 (2 x)}{16 (x^{1} x^{2})}$

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

$\frac{7}{16 x^{3}} - \frac{3 (2 x)}{16 x^{1 + 2}}$

Add $1$ and $2$ .

$\frac{7}{16 x^{3}} - \frac{3 (2 x)}{16 x^{3}}$

Step 3

Combine the numerators over the common denominator.

$\frac{7 - 3 (2 x)}{16 x^{3}}$

Step 4

Multiply $- 3$ by $2$ .

$\frac{7 - 6 x}{16 x^{3}}$