Simplify (x+5)/(x^2)-2/(5x)

$\frac{x + 5}{x^{2}} - \frac{2}{5 x}$

Step 1

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

$\frac{x + 5}{x^{2}} \cdot \frac{5}{5} - \frac{2}{5 x}$

Step 2

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

$\frac{x + 5}{x^{2}} \cdot \frac{5}{5} - \frac{2}{5 x} \cdot \frac{x}{x}$

Step 3

Write each expression with a common denominator of $5 x^{2}$ , by multiplying each by an appropriate factor of $1$ .

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

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

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

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

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

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

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

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

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

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

Add $1$ and $1$ .

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

Reorder the factors of $x^{2} \cdot 5$ .

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

Step 4

Combine the numerators over the common denominator.

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

Step 5

Simplify the numerator.

Apply the distributive property.

$\frac{x \cdot 5 + 5 \cdot 5 - 2 x}{5 x^{2}}$

Move $5$ to the left of $x$ .

$\frac{5 \cdot x + 5 \cdot 5 - 2 x}{5 x^{2}}$

Multiply $5$ by $5$ .

$\frac{5 \cdot x + 25 - 2 x}{5 x^{2}}$

Subtract $2 x$ from $5 x$ .

$\frac{3 x + 25}{5 x^{2}}$