Question

Rút gọn M=(x/x+3) + (2x/x-3) - (9-3x^2/9-x^2)

Answer 1

Đk \(x\ne\left\{-3;3\right\}\)

\(M=\frac{x}{x+3}+\frac{2x}{x-3}-\frac{9-3x^2}{9-x^2}\)

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

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

\(=\frac{x^2-3x+2x^2+6x+9-3x^2}{\left(x+3\right)\left(x-3\right)}\)

\(=\frac{3x+9}{\left(x+3\right)\left(x-3\right)}=\frac{3\left(x+3\right)}{\left(x+3\right)\left(x-3\right)}=\frac{3}{x-3}\)