a: \(x+\dfrac{3}{4\cdot7}+\dfrac{3}{7\cdot10}+...+\dfrac{3}{37\cdot40}=-\dfrac{37}{40}\)
=>\(x+\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+...+\dfrac{1}{37}-\dfrac{1}{40}=-\dfrac{37}{40}\)
=>\(x+\dfrac{1}{4}-\dfrac{1}{40}=-\dfrac{37}{40}\)
=>\(x+\dfrac{9}{40}=-\dfrac{37}{40}\)
=>\(x=-\dfrac{37}{40}-\dfrac{9}{40}=-\dfrac{46}{40}=-\dfrac{23}{20}\)
b: \(\dfrac{x-112}{116}+\dfrac{x-113}{115}+\dfrac{x-114}{114}+\dfrac{x-115}{113}=4\)
=>\(\left(\dfrac{x-112}{116}-1\right)+\left(\dfrac{x-113}{115}-1\right)+\left(\dfrac{x-114}{114}-1\right)+\left(\dfrac{x-115}{113}-1\right)=0\)
=>\(\dfrac{x-228}{116}+\dfrac{x-228}{115}+\dfrac{x-228}{114}+\dfrac{x-228}{113}=0\)
=>\(\left(x-228\right)\left(\dfrac{1}{116}+\dfrac{1}{115}+\dfrac{1}{114}+\dfrac{1}{113}\right)=0\)
=>x-228=0
=>x=228
