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

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

Step 1

Combine the numerators over the common denominator.

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

Step 2

Simplify each term.

Apply the distributive property.

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

Multiply $2$ by $- 1$ .

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

Multiply $- 1$ by $3$ .

$\frac{x - 2 x - 3}{4 x^{2}}$

Step 3

Simplify terms.

Subtract $2 x$ from $x$ .

$\frac{- x - 3}{4 x^{2}}$

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

$\frac{- (x) - 3}{4 x^{2}}$

Rewrite $- 3$ as $- 1 (3)$ .

$\frac{- (x) - 1 (3)}{4 x^{2}}$

Factor $- 1$ out of $- (x) - 1 (3)$ .

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

Simplify the expression.

Rewrite $- (x + 3)$ as $- 1 (x + 3)$ .

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

Move the negative in front of the fraction.

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