Simplify 8/(3x^2)+5/(4x)

$\frac{8}{3 x^{2}} + \frac{5}{4 x}$

To write $\frac{8}{3 x^{2}}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{8}{3 x^{2}} \cdot \frac{4}{4} + \frac{5}{4 x}$

To write $\frac{5}{4 x}$ as a fraction with a common denominator, multiply by $\frac{3 x}{3 x}$ .

$\frac{8}{3 x^{2}} \cdot \frac{4}{4} + \frac{5}{4 x} \cdot \frac{3 x}{3 x}$

Write each expression with a common denominator of $12 x^{2}$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{8}{3 x^{2}}$ by $\frac{4}{4}$ .

$\frac{8 \cdot 4}{3 x^{2} \cdot 4} + \frac{5}{4 x} \cdot \frac{3 x}{3 x}$

Multiply $4$ by $3$ .

$\frac{8 \cdot 4}{12 x^{2}} + \frac{5}{4 x} \cdot \frac{3 x}{3 x}$

Multiply $\frac{5}{4 x}$ by $\frac{3 x}{3 x}$ .

$\frac{8 \cdot 4}{12 x^{2}} + \frac{5 (3 x)}{4 x (3 x)}$

Multiply $3$ by $4$ .

$\frac{8 \cdot 4}{12 x^{2}} + \frac{5 (3 x)}{12 x \cdot x}$

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

$\frac{8 \cdot 4}{12 x^{2}} + \frac{5 (3 x)}{12 (x^{1} x)}$

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

$\frac{8 \cdot 4}{12 x^{2}} + \frac{5 (3 x)}{12 (x^{1} x^{1})}$

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

$\frac{8 \cdot 4}{12 x^{2}} + \frac{5 (3 x)}{12 x^{1 + 1}}$

Add $1$ and $1$ .

$\frac{8 \cdot 4}{12 x^{2}} + \frac{5 (3 x)}{12 x^{2}}$

Combine the numerators over the common denominator.

$\frac{8 \cdot 4 + 5 (3 x)}{12 x^{2}}$

Simplify the numerator.

Multiply $8$ by $4$ .

$\frac{32 + 5 \cdot 3 x}{12 x^{2}}$

Multiply $5$ by $3$ .

$\frac{32 + 15 x}{12 x^{2}}$