c: \(=\dfrac{4x+7+1}{\left(x+2\right)\left(4x+7\right)}=\dfrac{4\left(x+2\right)}{\left(x+2\right)\left(4x+7\right)}=\dfrac{4}{4x+7}\)
d: \(=\dfrac{\left(x+2\right)+1}{\left(x+3\right)\left(x+2\right)}+\dfrac{1}{\left(x+2\right)\left(4x+7\right)}\)
\(=\dfrac{1}{x+2}+\dfrac{1}{\left(x+2\right)\left(4x+7\right)}=\dfrac{4}{4x+7}\)
a: \(=\dfrac{y}{x\left(2x-y\right)}+\dfrac{4x}{y\left(y-2x\right)}\)
\(=\dfrac{y^2-4x^2}{xy\left(2x-y\right)}=\dfrac{-\left(2x-y\right)\left(2x+y\right)}{xy\left(2x-y\right)}=\dfrac{-2x-y}{xy}\)
b: \(=\dfrac{x^2-4+3\left(x+2\right)+x-14}{\left(x+2\right)^2\cdot\left(x-2\right)}=\dfrac{x^2+x-18+3x+6}{\left(x+2\right)^2\cdot\left(x-2\right)}\)
\(=\dfrac{x^2+4x-12}{\left(x+2\right)^2\cdot\left(x-2\right)}\)
=(x+6)(x-2)/(x+2)^2*(x-2)
=(x+6)/(x+2)^2
