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Lý thuyết Phân thức đại số SGK Toán 8 - Cùng khám phá

Phân thức đại số là gì?
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1. Khái niệm phân thức đại số

Một phân thức đại số (hay còn gọi là phân thứcಌ) là một biểu thức có dạng \(\frac{A}{B}\), trong đó A, B là những đa thức và B khác đa thức 0.

A được gọi là tử thức (hay tử), B được gọi là mẫu thức (hay mẫu).

Chú ý:🔴 Mỗi đa thức được coi là một phân thức với mẫu thức bằng 1.

Ví dụ: \(\frac{{2x + 1}}{{x - 3}};\frac{{ab}}{{a + b}};{x^2} + 3x + 2;\sqrt 2 \) là các phân thức đại số.\(\sqrt x ;\sqrt[3]{x}\) không phải là phân thức vì \(\sqrt x ;\sqrt[3]{x}\) không phải là đa thức.

2. Hai phân thức bằng nhau  

Hai  phân thức \(\frac{A}{B}\) và \(\frac{C}{D}\) bằng nhau𒁃, kí hiệu là \(\frac{A}{B} = \frac{C}{D}\) nếu A.D = B.C.

Ví dụ: Hai phân thức \(\frac{{x{y^2}}}{{xy + y}}\) và \(\frac{{xy}}{{x + 1}}\) bằng nhau.

3. Điều kiện xác định của phân thức \(\frac{A}{B}\) 

Điều kiện xác định🅘 của phân thức \(\frac{A}{B}\) là điều kiện của biến để mẫu thức B khác 0.

Để tính giá trị của phân thức ꧑tại giá trị cho trước của các biến (thỏa mãn điều kiện xác định của phân thức), ta thay giá trị các biến vào phân thức rồi thực hiện các phép tính.

Ví dụ: Phân thức P = \(\frac{{x + 3}}{{x - 1}}\) xác định khi \(x - 1 \ne 0\) hay \(x \ne 1\)Tại x = 3, \(P = \frac{{3 + 3}}{{3 - 1}} = \frac{6}{2} = 3\)

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