c,
\(\dfrac{3x^2+5x+14}{x^3+1}+\dfrac{x-1}{x^2-x+1}-\dfrac 4{x+1}\\ = \dfrac{3x^2+5x+14+(x-1)(x+1)-4(x^2-x+1)}{x^3+1}=\dfrac{3x^2+5x+14+x^2-1-4x^2+4x-4}{x^3+1}=\dfrac{9x+9}{(x+1)(x^2-x+1)}=\dfrac 9{x^2-x+1}\)
d,
\(\dfrac{5}{2x^2+6x}-\dfrac{4-3x^2}{x^2-9}-3=\dfrac{5(x-3)-2x(4-3x^2)-6x(x-3)(x+3)}{2x(x-3)(x+3)}=\dfrac{5x-15-8x+6x^3-6x(x^2-9)}{2x(x^2-9)}=\dfrac{51x-15}{2x^3-18x}\)
e,
\(A=\dfrac 1{x-3}-\dfrac 2{2x+6}-\dfrac x{2x^2-12x+18}=2(x^2-6x+9)\)
\(\to A=\dfrac{(x-3)(x+3)-(x-3)^2-0,5x}{(x-3)^2(x+3)}=\dfrac{x^2-9-x^2-9+6x-0,5x}{(x-3)^2(x+3)}=\dfrac{5,5x-18}{(x-3)(x+3)}=2(x-3)^2\to \dfrac{5,5x-18}{x+3}=2(x-3)\to x=\dfrac{11}4 \; x=0\)
