Simplify 1/4x+1+3/4x-2/3-1/2x

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

Step 1

Simplify each term.

Combine $\frac{1}{4}$ and $x$ .

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

Combine $\frac{3}{4}$ and $x$ .

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

Combine $x$ and $\frac{1}{2}$ .

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

Step 2

Simplify terms.

Combine the numerators over the common denominator.

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

Add $x$ and $3 x$ .

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

Step 3

Simplify each term.

Cancel the common factor of $4$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

$1 + x + \frac{- 2}{3} + \frac{- x}{2}$

Move the negative in front of the fraction.

$1 + x - \frac{2}{3} + \frac{- x}{2}$

Move the negative in front of the fraction.

$1 + x - \frac{2}{3} - \frac{x}{2}$

Step 4

Simplify the expression.

Write $1$ as a fraction with a common denominator.

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

Combine the numerators over the common denominator.

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

Subtract $2$ from $3$ .

$x + \frac{1}{3} - \frac{x}{2}$

Step 5

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

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

Step 6

Combine $x$ and $\frac{2}{2}$ .

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

Step 7

Combine the numerators over the common denominator.

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

Step 8

Subtract $x$ from $x \cdot 2$ .

Reorder $x$ and $2$ .

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

Subtract $x$ from $2 \cdot x$ .

$\frac{x}{2} + \frac{1}{3}$

Simplify 1/4x+1+3/4x-2/3-1/2x

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