\(C=\dfrac{1}{x+2}+\dfrac{1}{\left(x+2\right)\left(4x+7\right)}\\ C=\dfrac{4x+7}{\left(x+2\right)\left(\left(4x+7\right)\right)}+\dfrac{1}{\left(x+2\right)\left(4x+7\right)}\\ C=\dfrac{4x+7+1}{\left(x+2\right)\left(4x+7\right)}\\ C=\dfrac{4x+8}{\left(x+2\right)\left(4x+7\right)}\\ C=\dfrac{4\left(x+2\right)}{\left(x+2\right)\left(4x+7\right)}\\ C=\dfrac{4}{4x+7}\)
\(D=\dfrac{1-3x}{2x}+\dfrac{3x-2}{2x-1}+\dfrac{3x-2}{2x-4x^2}\\ D=\dfrac{1-3x}{2x}+\dfrac{3x-2}{2x-1}-\dfrac{3x-2}{4x^2-2x}\\ D=\dfrac{\left(1-3x\right)\left(2x-1\right)}{2x\left(2x-1\right)}+\dfrac{\left(3x-2\right)2x}{\left(2x-1\right)2x}-\dfrac{3x-2}{2x\left(2x-1\right)}\\ C=\dfrac{\left(1-3x\right)\left(2x-1\right)+\left(3x-2\right)2x-\left(3x-2\right)}{2x\left(2x-1\right)}\\ C=\dfrac{\left(1-3x\right)\left(2x-1\right)+\left[\left(3x-2\right)2x-\left(3x-2\right)\right]}{2x\left(2x-1\right)}\\ C=\dfrac{\left(1-3x\right)\left(2x-1\right)+\left(3x-2\right)\left(2x-1\right)}{2x\left(2x-1\right)}\\ C=\dfrac{\left[\left(1-3x\right)+\left(3x-2\right)\right]\left(2x-1\right)}{2x\left(2x-1\right)}\\ C=\dfrac{-\left(2x-1\right)}{2x\left(2x-1\right)}\\ C=-\dfrac{1}{2x}\)
