Question

(x^(3)+1)/(x-9)-(3x-9)/(x+3)-x

Answer 1

\(\dfrac{x^3+1}{x-9}-\dfrac{3x-9}{x+3}-x\)

\(=\dfrac{\left(x^3+1\right)\left(x+3\right)-\left(3x-9\right)\left(x-9\right)-x\left(x-9\right)\left(x+3\right)}{\left(x-9\right)\left(x+3\right)}\)

\(=\dfrac{x^4+3x^3+x+3-3x^2+27x+9x-81-x\left(x^2-6x-27\right)}{\left(x-9\right)\left(x+3\right)}\)

\(=\dfrac{x^4+37x-78-x^3+6x^2+27x}{\left(x-9\right)\left(x+3\right)}\)

\(=\dfrac{x^4-x^3+6x^2+64x-78}{\left(x-9\right)\left(x+3\right)}\)