Simplify (2x+1)/(6x^2)-(7x-2)/(6x^2)

$\frac{2 x + 1}{6 x^{2}} - \frac{7 x - 2}{6 x^{2}}$

Step 1

Combine the numerators over the common denominator.

$\frac{2 x + 1 - (7 x - 2)}{6 x^{2}}$

Step 2

Simplify each term.

Apply the distributive property.

$\frac{2 x + 1 - (7 x) - - 2}{6 x^{2}}$

Multiply $7$ by $- 1$ .

$\frac{2 x + 1 - 7 x - - 2}{6 x^{2}}$

Multiply $- 1$ by $- 2$ .

$\frac{2 x + 1 - 7 x + 2}{6 x^{2}}$

Step 3

Simplify terms.

Subtract $7 x$ from $2 x$ .

$\frac{- 5 x + 1 + 2}{6 x^{2}}$

Add $1$ and $2$ .

$\frac{- 5 x + 3}{6 x^{2}}$

Factor $- 1$ out of $- 5 x$ .

$\frac{- (5 x) + 3}{6 x^{2}}$

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

$\frac{- (5 x) - 1 (- 3)}{6 x^{2}}$

Factor $- 1$ out of $- (5 x) - 1 (- 3)$ .

$\frac{- (5 x - 3)}{6 x^{2}}$

Simplify the expression.

Rewrite $- (5 x - 3)$ as $- 1 (5 x - 3)$ .

$\frac{- 1 (5 x - 3)}{6 x^{2}}$

Move the negative in front of the fraction.

$- \frac{5 x - 3}{6 x^{2}}$