Question

Answer 1

a: \(=\dfrac{\left(x^2-1\right)\left(x^2+1\right)-2x\left(x^2-1\right)}{x^2-1}=x^2-2x+1=\left(x-1\right)^2\)

b: \(=\dfrac{\left(x^2-5\right)\left(x^2+5\right)+2x^3+10x-9x}{x^2+5}=x^2-5+2x+\dfrac{-9x}{x^2+5}\)

c: \(=\dfrac{6x^3+3x^2-4x^2-2x+3x+1.5-0.5}{2x+1}\)

\(=3x^2-2x+1.5+\dfrac{-0.5}{2x+1}\)

d: \(=\dfrac{x^4-2x^3+3x^2+x^3-2x^2+3x}{x^2-2x+3}=x^2+1\)

e: \(=\dfrac{\left(x+3\right)^2-y^2}{x+y+3}=x+3-y\)

f: \(=\dfrac{x^4-2x^3+2x^3-4x^2+4x^2-8x+7x-14}{x-2}=x^3+2x^2+4x+7\)