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Giải bài tập 3.38 trang 65 SGK Toán 9 tập 1 - Kết nối tri thức

Cho biểu thức (A = frac{{sqrt x + 2}}{{sqrt x - 2}} - frac{4}{{sqrt x + 2}}left( {x ge 0,x ne 4} right).) a) Rút gọn biểu thức A. b) Tính giá trị của A tại (x = 14.)

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

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Đề bài

Cho biểu thức \(A = \frac{{\sqrt x  + 2}}{{\sqrt x  - 2}} - \frac{4}{{\sqrt x  + 2}}\left( {x \ge 0,x \ne 4} \right).\) a) Rút gọn biểu thức A. b) Tính giá trị của A tại \(x = 14.\)

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

ꦓĐể rút gọn biểu thức ta cần quy đồng, mẫu số chung rồi rút gọn như đối với phân thức.

ౠKhi tính giá trị của biểu thức thì ta thay giá trị x cần tính vào biểu thức cần tính, cần kiểm tra điều kiện trước khi thay. 

Lời giải chi tiết

a) \(A = \frac{{\sqrt x  + 2}}{{\sqrt x  - 2}} - \frac{4}{{\sqrt x  + 2}}\left( {x \ge 0,x \ne 4} \right)\) \(\begin{array}{l}A = \frac{{{{\left( {\sqrt x  + 2} \right)}^2}}}{{\left( {\sqrt x  - 2} \right)\left( {\sqrt x  + 2} \right)}} - \frac{{4\left( {\sqrt x  - 2} \right)}}{{\left( {\sqrt x  + 2} \right)\left( {\sqrt x  - 2} \right)}}\\ = \frac{{x + 4\sqrt x  + 4 - 4\sqrt x  + 8}}{{\left( {\sqrt x  - 2} \right)\left( {\sqrt x  + 2} \right)}}\\ = \frac{{x  + 12}}{x-4}\end{array}\) b) Với \(x = 14\left( {t/m} \right)\) ta có \(A = \frac{{14  + 12}}{14-4} = \frac{{26 }}{{10}} = \frac{13 }{5}.\) Vậy \(x = 14\) thì \(A = \frac{{13}}{5}.\)

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