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Giải bài 9 trang 11 vở thực hành Toán 8 tập 2

Cho phân thức \(P = \frac{{{x^2} - 4x + 4}}{{{x^3} - 8}}\).

🌜Tổng hợp đề thi học kì 2 lớp 8 tất cả các môn - Kết nối tri thức

Toán - Văn - Anh - Khoa học tự nhiên
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Đề bài

💎Cho phân thức \(P = \frac{{{x^2} - 4x + 4}}{{{x^3} - 8}}\).

a) Kiểm tra xem x = -2 có thỏa mãn điều kiện xác định của P không. b) Rút gọn P và tính giá trị của P tại x = -2.

Phương pháp giải - Xem chi tiết

a) Thay x = -2 vào mẫu thức, nếu mẫu thức khác 0 thì x = -2 thỏa mãn điều kiện xác định của P và ngược lại. b) Muốn rút gọn một phân thức ta tìm nhân tử chung của tử thức và mẫu thức rồi chia cả tử và mẫu cho nhân tử chung đó. Thay x = -2 vào phân thức P, ta được giá trị của P.

Lời giải chi tiết

ꩲa) Điều kiện xác định P là \({x^3} - 8 \ne 0\). Khi \(x =  - 2\) thì \({x^3} - 8 = {\left( { - 2} \right)^3} - 8 =  - 8 - 8 =  - 16 \ne 0\) Do đó x = -2 thỏa mãn điều xác định của P.

𒊎b) Ta có: \(P = \frac{{{x^2} - 4x + 4}}{{{x^3} - 8}} = \frac{{{{(x - 2)}^2}}}{{(x - 2)({x^2} + 2x + 4)}} = \frac{{x - 2}}{{{x^2} + 2x + 4}}\)

🦂Thay x = -2 vào biểu thức P, ta được \(P = \frac{{ - 2 - 2}}{{{{\left( { - 2} \right)}^2} + 2\left( { - 2} \right) + 4}} = \frac{{ - 4}}{4} =  - 1\)

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