a) \(\dfrac{5xy^2-x^2y+4xy^2+5x^2y}{3xy}=\dfrac{9xy^2+4x^2y}{3xy}=\dfrac{xy\left(9y+4x\right)}{3xy}=\dfrac{9y+4x}{3}\)
b) \(\dfrac{x+3+x-1+x+4}{x+2}=\dfrac{3x+6}{x+2}=\dfrac{3\left(x+2\right)}{x+2}=3\)
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\(\dfrac{5xy^2-x^2y}{3xy}+\dfrac{4xy^2+5x^2y}{3xy}=\dfrac{5xy^2-x^2y+4xy^2+5x^2y}{3xy}=\dfrac{9xy^2+4x^2y}{3xy}=\dfrac{xy\left(9y+4x\right)}{3xy}=\dfrac{9y+4x}{3}\)
\(\dfrac{x+3}{x+2}+\dfrac{x-1}{x+2}+\dfrac{x+4}{x+2}=\dfrac{x+3+x-1+x+4}{x+2}=\dfrac{3x+6}{x+2}=\dfrac{3\left(x+2\right)}{x+2}=3\)
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