Question

Rút gọn biểu thức:\(\frac{x^2+5x+6+x\sqrt{9-x^2}}{3x-x^2+\left(x+2\right)\sqrt{9-x^2}}\)

Answer 1

\(=\frac{\left(x^2+5x+6\right)+x\sqrt{9-x^2}}{\left(3x-x^2\right)+\left(2+x\right)\sqrt{9-x^2}}\)

\(=\frac{\left(x+2\right)\left(3+x\right)+x\sqrt{\left(3+x\right)\left(3-x\right)}}{x\left(3-x\right)+\left(x+2\right)\sqrt{\left(3+x\right)\left(3-x\right)}}\) nhóm nhân tử chung

\(=\frac{\sqrt{3+x}\left(\left(x+2\right)\sqrt{3+x}+x\sqrt{3-x}\right)}{\sqrt{3-x}\left(x\sqrt{3-x}+\left(x+2\right)\sqrt{3+x}\right)}\)rồi rút gọn được

\(=\frac{\sqrt{3+x}}{\sqrt{3-x}}\)