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Giải mục 1 trang 8, 9 SGK Toán 8 tập 2 - Kết nối tri thức

Nếu nhân cả tử và mẫu của phân thức

🦋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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HĐ 1

Video hướng dẫn giải

Nếu nhân cả tử và mẫu của phân thức \(\frac{{x + y}}{{x - y}}\) với 2x ta được phân thức mới nào? Giải thích vì sao phân thức mới nhận được bằng phân thức đã cho. 

Phương pháp giải:

Thực hiện theo yêu cầu của đề bài

Lời giải chi tiết:

Nhân cả tử và mẫu của phân thức \(\frac{{x + y}}{{x - y}}\) với 2x, ta có: \(\frac{{2{\rm{x}}\left( {x + y} \right)}}{{2{\rm{x}}\left( {x - y} \right)}}\) Phân thức mới nhận được bằng phân thức đã cho vì cả tử và mẫu của phân thức đều nhân cùng với một số.

HĐ 2

Video hướng dẫn giải

Tử và mẫu của phân thức \(\frac{{\left( {x - 1} \right)\left( {x + 1} \right)}}{{\left( {x - 1} \right)\left( {{x^2} + x + 1} \right)}}\)có nhân tử chung là x−1. Viết phân thức nhận được sau khi chia cả tử và mẫu của phân thức này cho nhân tử chung đó. So sánh phân thức mới nhận được với phân thức đã cho. 

Phương pháp giải:

Thực hiện theo yêu cầu của đề bài

Lời giải chi tiết:

Chia cả tử và mẫu của phân thức này cho nhân tử chung x−1, ta có \(\frac{{x + 1}}{{{x^2} + x + 1}}\) => Phân thức mới được rút gọn và mất đi nhân tử chung x−1 

LT 1

Video hướng dẫn giải

Khẳng định sau đúng hay sai? Vì sao?

෴\(\frac{{30{\rm{x}}{y^2}\left( {x - y} \right)}}{{45{\rm{x}}y{{\left( {x - y} \right)}^2}}} = \frac{{2y}}{{3\left( {x - y} \right)}}\)

Phương pháp giải:

Nhân cả tử và mẫu của phân thức \(\frac{{2y}}{{3\left( {x - y} \right)}}\) với 15 

Lời giải chi tiết:

Khẳng định trên là đúng. Vì nhân cả tử và mẫu của phân thức \(\frac{{2y}}{{3\left( {x - y} \right)}}\) với 15 ta được phân thức \(\frac{{30{\rm{x}}{y^2}\left( {x - y} \right)}}{{45{\rm{x}}y{{\left( {x - y} \right)}^2}}} \Rightarrow \frac{{30{\rm{x}}{y^2}\left( {x - y} \right)}}{{45{\rm{x}}y{{\left( {x - y} \right)}^2}}} = \frac{{2y}}{{3\left( {x - y} \right)}}\)

LT 2

Video hướng dẫn giải

Giải thích vì sao \(\frac{{ - x}}{{1 - x}} = \frac{x}{{x - 1}}\)

Phương pháp giải:

Nhân cả tử và mẫu của phân thức \(\frac{x}{{x - 1}}\) với -1

Lời giải chi tiết:

Nhân cả tử và mẫu của phân thức \(\frac{x}{{x - 1}}\) với -1 ta được phân thức \(\frac{{ - x}}{{1 - x}} \Rightarrow \frac{{ - x}}{{1 - x}} = \frac{x}{{x - 1}}\)

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