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Giải bài tập 3.22 trang 59 SGK Toán 9 tập 1 - Kết nối tri thức

Rút gọn biểu thức (A = sqrt x left( {frac{1}{{sqrt x + 3}} - frac{1}{{3 - sqrt x }}} right)left( {x ge 0,x ne 9} right).)

Tổng hợp Đề thi vào 10 có đáp án và lời giải

Toán - Văn - Anh
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Đề bài

🧸Rút gọn biểu thức \(A = \sqrt x \left( {\frac{1}{{\sqrt x  + 3}} - \frac{1}{{3 - \sqrt x }}} \right)\left( {x \ge 0,x \ne 9} \right).\)

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

🌊Đối với biểu thức trên ta có thể sử dụng trục căn thức ở mẫu. Rồi quy đồng mẫu rồi cộng trừ như cộng trừ phân thức.

Lời giải chi tiết

\(\begin{array}{l}A = \sqrt x \left( {\frac{1}{{\sqrt x  + 3}} - \frac{1}{{3 - \sqrt x }}} \right)\\ = \sqrt x .\left( {\frac{{\sqrt x  - 3}}{{x - 9}} - \frac{{3 + \sqrt x }}{{9 - x}}} \right)\\ = \sqrt x .\left( {\frac{{\sqrt x  - 3}}{{x - 9}} + \frac{{3 + \sqrt x }}{{x - 9}}} \right)\\ = \sqrt x \left( {\frac{{\sqrt x  - 3 + 3 + \sqrt x }}{{x - 9}}} \right)\\ = \sqrt x .\frac{2\sqrt x}{x-9} \\ = \frac{2x}{x-9}\end{array}\)

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