Solve x-1/2+1+x-2/3+2=

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

Evaluate

$$\frac{5x+11}{6}$$

Short Solution Steps

Add 1 and 2 to get 3.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{2}{2}.

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

Since \frac{x-1}{2} and \frac{3\times 2}{2} have the same denominator, add them by adding their numerators.

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

Do the multiplications in x-1+3\times 2.

$$\frac{x-1+6}{2}+\frac{x-2}{3}$$

Combine like terms in x-1+6.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 3 is 6. Multiply \frac{x+5}{2} times \frac{3}{3}. Multiply \frac{x-2}{3} times \frac{2}{2}.

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

Since \frac{3\left(x+5\right)}{6} and \frac{2\left(x-2\right)}{6} have the same denominator, add them by adding their numerators.

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

Do the multiplications in 3\left(x+5\right)+2\left(x-2\right).

$$\frac{3x+15+2x-4}{6}$$

Combine like terms in 3x+15+2x-4.

$$\frac{5x+11}{6}$$

Expand

$$\frac{5x+11}{6}$$

Short Solution Steps

Add 1 and 2 to get 3.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{2}{2}.

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

Since \frac{x-1}{2} and \frac{3\times 2}{2} have the same denominator, add them by adding their numerators.

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

Do the multiplications in x-1+3\times 2.

$$\frac{x-1+6}{2}+\frac{x-2}{3}$$

Combine like terms in x-1+6.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 3 is 6. Multiply \frac{x+5}{2} times \frac{3}{3}. Multiply \frac{x-2}{3} times \frac{2}{2}.

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

Since \frac{3\left(x+5\right)}{6} and \frac{2\left(x-2\right)}{6} have the same denominator, add them by adding their numerators.

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

Do the multiplications in 3\left(x+5\right)+2\left(x-2\right).

$$\frac{3x+15+2x-4}{6}$$

Combine like terms in 3x+15+2x-4.

$$\frac{5x+11}{6}$$