\(\dfrac{5}{1\cdot4}+\dfrac{5}{4\cdot7}+\dfrac{5}{7\cdot11}+...+\dfrac{5}{\left(3x+1\right)\cdot\left(3x+4\right)}\\ =\dfrac{5}{3}\cdot\left(\dfrac{3}{1\cdot4}+\dfrac{3}{4\cdot7}+\dfrac{3}{7\cdot11}+...+\dfrac{3}{\left(3x+1\right)\cdot\left(3x+4\right)}\right)\\ =\dfrac{5}{3}\cdot\left(1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{11}+...+\dfrac{1}{3x+1}-\dfrac{1}{3x+4}\right)\\ =\dfrac{5}{3}\cdot\left(1-\dfrac{1}{3x+4}\right)\\ =\dfrac{5}{3}-\dfrac{5}{9x+12}\)
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