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

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

To write $\frac{5 x}{4}$ as a fraction with a common denominator, multiply by $\frac{x^{2}}{x^{2}}$ .

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

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

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

Write each expression with a common denominator of $4 x^{2}$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{5 x}{4}$ by $\frac{x^{2}}{x^{2}}$ .

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

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

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

Reorder the factors of $x^{2} \cdot 4$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $x$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

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

Multiply $x^{2}$ by $x$ .

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

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

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

$\frac{5 x^{2 + 1} + 3 \cdot 4}{4 x^{2}}$

Add $2$ and $1$ .

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

Multiply $3$ by $4$ .

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