11:
\(=\dfrac{7x+6}{\left(x-2\right)\left(x+2\right)}+\dfrac{x+1}{x-2}+\dfrac{x}{x+2}\)
\(=\dfrac{7x+6+\left(x+1\right)\left(x+2\right)+x\left(x-2\right)}{\left(x-2\right)\left(x+2\right)}\)
\(=\dfrac{7x+6+x^2+3x+2+x^2-2x}{\left(x-2\right)\left(x+2\right)}=\dfrac{2x^2+8x+8}{\left(x-2\right)\left(x+2\right)}\)
\(=\dfrac{2\left(x+2\right)^2}{\left(x-2\right)\left(x+2\right)}=\dfrac{2\left(x+2\right)}{x-2}=\dfrac{2x+4}{x-2}\)
12:
\(=\dfrac{4-x^2+\left(x-2\right)\left(x+2\right)+2x\left(x^2-2x+4\right)}{\left(x+2\right)\left(x^2-2x+4\right)}\)
\(=\dfrac{2x\left(x^2-2x+4\right)}{\left(x+2\right)\left(x^2-2x+4\right)}=\dfrac{2x}{x+2}\)
14:
\(=\dfrac{2x^3-x-x^3-3+x+2}{x-1}=\dfrac{x^3-1}{x-1}=x^2+x+1\)
