a) \(\dfrac{5x-2}{15}+\dfrac{2x+2}{15}\)
\(=\dfrac{5x-2+2x+2}{15}\)
\(=\dfrac{7x}{15}\)
b) \(\dfrac{2-2x}{6x^3y}+\dfrac{3+2y}{6x^3y}+\dfrac{2x-5}{6x^3y}\)
\(=\dfrac{2-2x+3+2y+2x-5}{6x^3y}\)
\(=\dfrac{2y}{6x^3y}\)
\(=\dfrac{1}{3x^3}\)
c) \(\dfrac{x^2}{x+y}+\dfrac{y^2}{y+z}+\dfrac{-y^2}{x+y}+\dfrac{-z^2}{y+z}\)
\(=\dfrac{x^2-y^2}{x+y}+\dfrac{y^2-z^2}{y+z}\)
\(=\dfrac{\left(x+y\right)\left(x-y\right)}{x+y}+\dfrac{\left(y+z\right)\left(y-z\right)}{y+z}\)
\(=x-y+y-z\)
\(=x-z\)
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