\(A=\dfrac{3x^2-11x-14}{4x^2+7x+3}=\dfrac{3x^2+3x-14x-14}{4x^2+4x+3x+3}=\dfrac{3x\left(x+1\right)-14\left(x+1\right)}{4\left(x+1\right)+3\left(x+1\right)}\\ =\dfrac{\left(x+1\right)\left(3x-14\right)}{\left(x+1\right).\left(4+3\right)}=\dfrac{3x-14}{7}\)
\(B=\dfrac{x^2+13x-7x-91}{x^2+15x-7x-105}=\dfrac{x\left(x+13\right)-7\left(x+13\right)}{x\left(x+15\right)-7\left(x+15\right)}=\dfrac{\left(x-7\right)\left(x+13\right)}{\left(x-7\right)\left(x+15\right)}\\ =\dfrac{x+13}{x+15}\)
\(C=\dfrac{x^3-6x^2+11x-6}{x^2-3x+2}=\dfrac{x^3-3x^2+2x-3x^2+9x-6}{x^2-3x+2}\\ =\dfrac{x\left(x^2-3x+2\right)-3\left(x^2-3x+2\right)}{x^2-3x+2}=\dfrac{\left(x-3\right)\left(x^2-3x+2\right)}{x^2-3x+2}=x-3\)
\(A=\dfrac{3x^2-11x-14}{4x^2+7x+3}\)
\(=\dfrac{3x^2-14x+3x-14}{4x^2+4x+3x+3}\)
\(=\dfrac{x\left(3x-14\right)+\left(3x-14\right)}{\left(x+1\right)\left(4x+3\right)}=\dfrac{\left(x+1\right)\left(3x-14\right)}{\left(x+1\right)\left(4x+3\right)}=\dfrac{3x-14}{4x+3}\)
\(B=\dfrac{x^2+6x-91}{x^2+8x-105}\)
\(=\dfrac{x^2+13x-7x-91}{x^2+15x-7x-105}\)
\(=\dfrac{x\left(x+13\right)-7\left(x+13\right)}{x\left(x+15\right)-7\left(x+15\right)}\)
\(=\dfrac{\left(x+13\right)\left(x-7\right)}{\left(x+15\right)\left(x-7\right)}=\dfrac{x+13}{x+15}\)
\(C=\dfrac{x^3-6x^2+11x-6}{x^2-3x+2}\)
\(=\dfrac{x^3-x^2-5x^2+5x+6x-6}{\left(x-1\right)\left(x-2\right)}\)
\(=\dfrac{\left(x-1\right)\left(x^2-5x+6\right)}{\left(x-1\right)\left(x-2\right)}=\dfrac{x^2-5x+6}{x-2}\)
\(=\dfrac{\left(x-2\right)\left(x-3\right)}{x-2}=x-3\)
