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Giải bài 5 trang 10 vở thực hành Toán 8 tập 2

Tìm a sao cho hai phân thức sau bằng nhau: \(\frac{{5x}}{{x + 1}}\) và \(\frac{{ax(x - 1)}}{{(1 - x)(x + 1)}}\).

♏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

꧋Tìm a sao cho hai phân thức sau bằng nhau: \(\frac{{5x}}{{x + 1}}\) và \(\frac{{ax(x - 1)}}{{(1 - x)(x + 1)}}\).

Phương pháp giải - Xem chi tiết

Dựa vào tính chất cơ bản của phân thức đại số - Nếu nhân cả tử và mẫu của một phân thức với cùng một đa thức khác 0 thì được một phân thức bằng phân thức đã cho. - Nếu chia cả tử và mẫu của một phân thức cho một nhân tử chung của chúng thì được một phân thức bằng phân thức đã cho.

Lời giải chi tiết

🎃Chia cả tử và mẫu của phân thức \(\frac{{ax(x - 1)}}{{(1 - x)(x + 1)}}\) cho 1 – x = - (x – 1), ta được:

ಌ\(\frac{{ax(x - 1)}}{{(1 - x)(x + 1)}} = \frac{{ - ax}}{{x + 1}}\) .

✤Vì vậy cần tìm a sao cho \(\frac{{5x}}{{x + 1}} = \frac{{ - ax}}{{x + 1}}\). Do đó –a = 5, hay a = -5.

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