Question

Câu 4: Cho biểu thức : \(A=\left(\frac{1}{\sqrt{1+x}}+\sqrt{1-x}\right):\left(\frac{1}{\sqrt{1-x^2}}+1\right)\)

a.Tìm x để biểu thức A có nghĩa

b.Rút gọn A

Answer 1

a) ĐKXĐ: \(-1\le x< 1\)

b) Ta có: \(A=\left(\frac{1}{\sqrt{1+x}}+\sqrt{1-x}\right):\left(\frac{1}{\sqrt{1-x^2}}+1\right)\)

\(=\left(\frac{1}{\sqrt{1+x}}+\frac{\sqrt{1-x}\cdot\sqrt{1+x}}{\sqrt{1+x}}\right):\left(\frac{1}{\sqrt{1-x}\cdot\sqrt{1+x}}+\frac{\sqrt{1-x}\cdot\sqrt{1+x}}{\sqrt{1-x}\cdot\sqrt{1+x}}\right)\)

\(=\frac{1+\sqrt{1-x^2}}{\sqrt{1+x}}\cdot\frac{\sqrt{1-x}\cdot\sqrt{1+x}}{1+\sqrt{1-x^2}}\)

\(=\sqrt{1-x}\)