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Giải mục 4 trang 18, 19 SGK Toán 8 tập 2 - Kết nối tri thức

Rút gọn biểu 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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LT 4

Video hướng dẫn giải

Rút gọn biểu thức: \(P = \frac{1}{x} + \frac{1}{y} + \frac{1}{z} - \frac{1}{x} - \frac{1}{y}\)

Phương pháp giải:

Nhóm các số có cùng mẫu để thực hiện phép tính

Lời giải chi tiết:

Ta có: \(\begin{array}{l}P = \frac{1}{x} + \frac{1}{y} + \frac{1}{z} - \frac{1}{x} - \frac{1}{y}\\P = \left( {\frac{1}{x} - \frac{1}{x}} \right) + \left( {\frac{1}{y} - \frac{1}{y}} \right) + \frac{1}{z} = 0 + 0 + \frac{1}{z} = \frac{1}{z}\end{array}\)

LT 5

Video hướng dẫn giải

Đề bài đưa ra: hãy rút gọn biểu thức: \(P = \frac{x}{{x + 1}} - \left[ {\left( {\frac{1}{{x - 1}} + \frac{x}{{x + 1}}} \right) - \frac{1}{{x - 1}}} \right]\) Vuông: Không cần tính toán, em thấy ngay kết quả P = 0 Tròn: Làm thế nào mà Vuông thấy ngay được kết quả thế nhỉ?

Phương pháp giải:

Thực hiện theo quy tắc cộng, trừ các phân thức đại số

Lời giải chi tiết:

\(\begin{array}{l}P = \frac{x}{{x + 1}} - \left[ {\left( {\frac{1}{{x - 1}} + \frac{x}{{x + 1}}} \right) - \frac{1}{{x - 1}}} \right]\\P = \frac{x}{{x + 1}} - \left[ {\frac{1}{{x - 1}} + \frac{x}{{x + 1}} - \frac{1}{{x - 1}}} \right]\\P = \frac{x}{{x + 1}} - \frac{x}{{x + 1}} = 0\end{array}\) Vì vuông đã sử dụng phép cộng, phép trừ phân thức đại số.

VD

Video hướng dẫn giải

🐽Chú Đức lái ô tô từ Hà Nội về quê. Từ nhà chú đến đường cao tốc dài khoảng 20km, xe chạy trong thành phố với vận tốc x(km/h) (x>0). Trên 50km đường cao tốc, xe tăng vận tốc thêm 55km/h. Ra khỏi cao tốc, xe còn phải chạy thêm 15 phút thì về đến quê

🐟a) Viết các phân thức biểu thị thời gian xe chạy trong thành phố và thời gian xe chạy trên đường cao tốc

🐈b) Viết phân thức biểu thị tổng thời gian chú Đức đi từ Hà Nội về quê

Phương pháp giải:

Viết phân thức biểu thị theo yêu cầu của đề bài: Thời gian bằng quãng đường chia cho vận tốc

Lời giải chi tiết:

a) Phân thức biểu thị thời gian xe chạy trong thành phố: \({t_1} = \frac{{20}}{x}\) (giờ) Phân thức biểu thị thời gian xe chạy trên đường cao tốc: \({t_2} = \frac{{50}}{{x + 55}}\) (giờ) b)Phân thức biểu thị tổng thời gian chú Đức đi từ Hà Nội về quê:

\(\begin{array}{l}{t_1} + {t_2} + \frac{1}{4}\\ = \frac{{20}}{x} + \frac{{50}}{{x + 55}} + \frac{1}{4}\\ = \frac{{80\left( {x + 55} \right) + 200{\rm{x}} + x\left( {x + 55} \right)}}{{4{\rm{x}}\left( {x + 55} \right)}} = \frac{{{x^2} + 335{\rm{x}} + 4400}}{{4{\rm{x}}\left( {x + 55} \right)}}\end{array}\)

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