Question

\(\dfrac{2x}{x+3}\)+\(\dfrac{x+1}{x-3}\)-\(\dfrac{3-11x}{x^2-9}\)

Answer 1

ĐKXĐ: \(x\notin\left\{3;-3\right\}\)

\(\dfrac{2x}{x+3}+\dfrac{x+1}{x-3}-\dfrac{3-11x}{x^2-9}\)

\(=\dfrac{2x}{x+3}+\dfrac{x+1}{x-3}+\dfrac{11x-3}{\left(x-3\right)\left(x+3\right)}\)

\(=\dfrac{2x\left(x-3\right)+\left(x+1\right)\left(x+3\right)+11x-3}{\left(x+3\right)\left(x-3\right)}\)

\(=\dfrac{2x^2-6x+x^2+4x+3+11x-3}{\left(x+3\right)\left(x-3\right)}\)

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