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\frac{2\times 2x}{2}-\frac{x-y}{2}-\frac{x-2y}{3}
To add or subtract expressions, expand them to make their denominators the same. Multiply 2x times \frac{2}{2}.
\frac{2\times 2x-\left(x-y\right)}{2}-\frac{x-2y}{3}
Since \frac{2\times 2x}{2} and \frac{x-y}{2} have the same denominator, subtract them by subtracting their numerators.
\frac{4x-x+y}{2}-\frac{x-2y}{3}
Do the multiplications in 2\times 2x-\left(x-y\right).
\frac{3x+y}{2}-\frac{x-2y}{3}
Combine like terms in 4x-x+y.
\frac{3\left(3x+y\right)}{6}-\frac{2\left(x-2y\right)}{6}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 3 is 6. Multiply \frac{3x+y}{2} times \frac{3}{3}. Multiply \frac{x-2y}{3} times \frac{2}{2}.
\frac{3\left(3x+y\right)-2\left(x-2y\right)}{6}
Since \frac{3\left(3x+y\right)}{6} and \frac{2\left(x-2y\right)}{6} have the same denominator, subtract them by subtracting their numerators.
\frac{9x+3y-2x+4y}{6}
Do the multiplications in 3\left(3x+y\right)-2\left(x-2y\right).
\frac{7x+7y}{6}
Combine like terms in 9x+3y-2x+4y.
\frac{2\times 2x}{2}-\frac{x-y}{2}-\frac{x-2y}{3}
To add or subtract expressions, expand them to make their denominators the same. Multiply 2x times \frac{2}{2}.
\frac{2\times 2x-\left(x-y\right)}{2}-\frac{x-2y}{3}
Since \frac{2\times 2x}{2} and \frac{x-y}{2} have the same denominator, subtract them by subtracting their numerators.
\frac{4x-x+y}{2}-\frac{x-2y}{3}
Do the multiplications in 2\times 2x-\left(x-y\right).
\frac{3x+y}{2}-\frac{x-2y}{3}
Combine like terms in 4x-x+y.
\frac{3\left(3x+y\right)}{6}-\frac{2\left(x-2y\right)}{6}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 3 is 6. Multiply \frac{3x+y}{2} times \frac{3}{3}. Multiply \frac{x-2y}{3} times \frac{2}{2}.
\frac{3\left(3x+y\right)-2\left(x-2y\right)}{6}
Since \frac{3\left(3x+y\right)}{6} and \frac{2\left(x-2y\right)}{6} have the same denominator, subtract them by subtracting their numerators.
\frac{9x+3y-2x+4y}{6}
Do the multiplications in 3\left(3x+y\right)-2\left(x-2y\right).
\frac{7x+7y}{6}
Combine like terms in 9x+3y-2x+4y.