Simplify (x-5)/(x^2+25)-3x

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

To write $- 3 x$ as a fraction with a common denominator, multiply by $\frac{x^{2} + 25}{x^{2} + 25}$ .

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

Simplify terms.

Combine $- 3 x$ and $\frac{x^{2} + 25}{x^{2} + 25}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Apply the distributive property.

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

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

Move $x^{2}$ .

$\frac{x - 5 - 3 (x^{2} x) - 3 x \cdot 25}{x^{2} + 25}$

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

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

$\frac{x - 5 - 3 (x^{2} x^{1}) - 3 x \cdot 25}{x^{2} + 25}$

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

$\frac{x - 5 - 3 x^{2 + 1} - 3 x \cdot 25}{x^{2} + 25}$

Add $2$ and $1$ .

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

Multiply $25$ by $- 3$ .

$\frac{x - 5 - 3 x^{3} - 75 x}{x^{2} + 25}$

Subtract $75 x$ from $x$ .

$\frac{- 74 x - 5 - 3 x^{3}}{x^{2} + 25}$

Reorder terms.

$\frac{- 3 x^{3} - 74 x - 5}{x^{2} + 25}$

Simplify with factoring out.

Factor $- 1$ out of $- 3 x^{3}$ .

$\frac{- (3 x^{3}) - 74 x - 5}{x^{2} + 25}$

Factor $- 1$ out of $- 74 x$ .

$\frac{- (3 x^{3}) - (74 x) - 5}{x^{2} + 25}$

Factor $- 1$ out of $- (3 x^{3}) - (74 x)$ .

$\frac{- (3 x^{3} + 74 x) - 5}{x^{2} + 25}$

Rewrite $- 5$ as $- 1 (5)$ .

$\frac{- (3 x^{3} + 74 x) - 1 (5)}{x^{2} + 25}$

Factor $- 1$ out of $- (3 x^{3} + 74 x) - 1 (5)$ .

$\frac{- (3 x^{3} + 74 x + 5)}{x^{2} + 25}$

Simplify the expression.

Rewrite $- (3 x^{3} + 74 x + 5)$ as $- 1 (3 x^{3} + 74 x + 5)$ .

$\frac{- 1 (3 x^{3} + 74 x + 5)}{x^{2} + 25}$

Move the negative in front of the fraction.

$- \frac{3 x^{3} + 74 x + 5}{x^{2} + 25}$