(1(1))/(x-2y)-(1(1))/(4y-2x)+((1))/(3x-6y)

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Identify Fractions: Identify the expressions to be combined and note that they are fractions that need a common denominator.Simplify Denominators: Recognize that the denominators (x-2y), (4y-2x), and (3x-6y) can be simplified and made common. Notice that (4y-2x) is -(x-2y) multiplied by 2, and (3x-6y) is (x-2y) multiplied by 3.Find LCD: Find the least common denominator (LCD) for the three fractions. The LCD for (x-2y), -(2(x-2y)), and 3(x-2y) is 6(x-2y).Rewrite with LCD: Rewrite each fraction with the common denominator 6(x-2y). The first fraction is already (1/(x-2y)), so it needs to be multiplied by 6/6 to get the common denominator. The second fraction is (1/(-2(x-2y))), so it needs to be multiplied by -3/-3 to get the common denominator. The third fraction is (1/(3(x-2y))), so it needs to be multiplied by 2/2 to get the common denominator.Multiply by 1: Multiply each fraction by the appropriate form of 1 to get the common denominator: (1/(x-2y)) * (6/6) = 6/(6(x-2y)) (1/(4y-2x)) * (-3/-3) = -3/(6(x-2y)) (1/(3x-6y)) * (2/2) = 2/(6(x-2y))Combine Fractions: Combine the fractions now that they have a common denominator: 6/(6(x-2y)) - (-3/(6(x-2y))) + 2/(6(x-2y))Add and Subtract Numerators: Add and subtract the numerators: 6 - (-3) + 2 = 6 + 3 + 2 = 11Write Combined Fraction: Write the combined fraction with the common denominator: 11/(6(x-2y))

$\frac{1(1)}{x-2 y}-\frac{1(1)}{4 y-2 x}+\frac{(1)}{3 x-6 y}$

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1(1)x−2y−1(1)4y−2x+(1)3x−6y \frac{1(1)}{x-2 y}-\frac{1(1)}{4 y-2 x}+\frac{(1)}{3 x-6 y} x−2y1(1)​−4y−2x1(1)​+3x−6y(1)​

$\frac{1(1)}{x-2 y}-\frac{1(1)}{4 y-2 x}+\frac{(1)}{3 x-6 y}$