Cho biểu thức $C = \dfrac{{2\sqrt x - 9}}{{x - 5\sqrt x + 6}} - \dfrac{{\sqrt x + 3}}{{\sqrt x - 2}} - \dfrac{{2\sqrt x + 1}}{{3 - \sqrt x }}$
với $x \ge 0;x \ne 4;x \ne 9$.
Rút gọn biểu thức $C$ ta được
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A.
$C = \dfrac{{\sqrt x - 1}}{{\sqrt x - 3}}$
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B.
$C = \dfrac{{\sqrt x - 1}}{{\sqrt x + 3}}$
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C.
$C = \dfrac{{\sqrt x + 1}}{{\sqrt x - 3}}$
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D.
$C = \dfrac{{\sqrt x + 1}}{{\sqrt x + 3}}$
Đáp án : C
-Tìm mẫu thức chung bằng cách phân tích đa thức thành nhân tử
-Quy đồng mẫu thức các phân thức.
-Cộng trừ các phân thức đã quy đồng và rút gọn.
Ta có $x - 5\sqrt x + 6 = x - 2\sqrt x - 3\sqrt x + 6 = \sqrt x \left( {\sqrt x - 2} \right) - 3\left( {\sqrt x - 2} \right) = \left( {\sqrt x - 3} \right)\left( {\sqrt x - 2} \right)$ nên
$C = \dfrac{{2\sqrt x - 9}}{{x - 5\sqrt x + 6}} - \dfrac{{\sqrt x + 3}}{{\sqrt x - 2}} - \dfrac{{2\sqrt x + 1}}{{3 - \sqrt x }}$$ = \dfrac{{2\sqrt x - 9}}{{\left( {\sqrt x - 2} \right)\left( {\sqrt x - 3} \right)}} - \dfrac{{\sqrt x + 3}}{{\sqrt x - 2}} + \dfrac{{2\sqrt x + 1}}{{\sqrt x - 3}}$
$ = \dfrac{{2\sqrt x - 9 - \left( {\sqrt x + 3} \right)\left( {\sqrt x - 3} \right) + \left( {2\sqrt x + 1} \right)\left( {\sqrt x - 2} \right)}}{{\left( {\sqrt x - 2} \right)\left( {\sqrt x - 3} \right)}}$$ = \dfrac{{2\sqrt x - 9 - x + 9 + 2x - 3\sqrt x - 2}}{{\left( {\sqrt x - 2} \right)\left( {\sqrt x - 3} \right)}}$
$ = \dfrac{{x - \sqrt x - 2}}{{\left( {\sqrt x - 2} \right)\left( {\sqrt x - 3} \right)}} = \dfrac{{x - 2\sqrt x + \sqrt x - 2}}{{\left( {\sqrt x - 2} \right)\left( {\sqrt x - 3} \right)}} = \dfrac{{\sqrt x \left( {\sqrt x - 2} \right) + \left( {\sqrt x - 2} \right)}}{{\left( {\sqrt x - 2} \right)\left( {\sqrt x - 3} \right)}} = \dfrac{{\left( {\sqrt x + 1} \right)\left( {\sqrt x - 2} \right)}}{{\left( {\sqrt x - 2} \right)\left( {\sqrt x - 3} \right)}} = \dfrac{{\sqrt x + 1}}{{\sqrt x - 3}}$
Vậy $C = \dfrac{{\sqrt x + 1}}{{\sqrt x - 3}}$với $x \ge 0;x \ne 4;x \ne 9$
Các bài tập cùng chuyên đề
Choose the word which has the underlined part pronounced differently from the rest.
Choose the word which has the underlined part pronounced differently from the rest.
Choose the word which has the underlined part pronounced differently from the rest.
Choose the word which has the underlined part pronounced differently from the rest.
Choose the word which has the underlined part pronounced differently from the rest.
Choose the word which has the underlined part pronounced differently from the rest.
Choose the word which has the underlined part pronounced differently from the rest.
Choose the word which has the underlined part pronounced differently from the rest.
Diphthong /eɪ/ and /əʊ/
(Nguyên âm đôi /eɪ/ và /əʊ/)
1. Listen and repeat. Then practise saying the words.
(Lắng nghe và lặp lại. Sau đó thực hành nói các từ.)
|
/eɪ/ |
/əʊ/ |
|
age /eɪdʒ/ |
soldier /ˈsəʊldʒə(r)/ |
|
saved /seɪvd/ |
wrote /rəʊt/ |
|
translated /trænzˈleɪtɪd/ |
hero /ˈhɪərəʊ/ |
|
against /əˈɡenst/ |
shows /ʃəʊz/ |
2. Work in pairs. Underline the words that contain the /eɪ/ and /əʊ/ sounds. Listen and check. Then practise reading the whole text aloud.
(Làm việc theo cặp. Gạch dưới những từ có chứa âm /eɪ/ và /əʊ/. Nghe và kiểm tra. Sau đó thực hành đọc to toàn bộ văn bản.)
In the first year when The Diary of Dang Thuy Tram was published, more than 300,000 copies were sold. The book was also translated into more than 16 different languages. A film based on the diary was made in 2009. Its name is Don't burn.
Underline the words that contain the /eɪ/ sound and circle the ones with the /əʊ/ sound in the sentences below. Then listen and check. Practise saying these sentences in pairs.
(Gạch chân những từ có chứa âm /eɪ/ và khoanh tròn những từ có âm /əʊ/ trong các câu dưới đây. Sau đó nghe và kiểm tra. Thực hành nói những câu này theo cặp.)
1. Cleopatra VII, a queen of ancient Egypt, was famous for her beauty.
2. I love Disney animated films like Snow White and the Seven Dwarfs and The Little Mermaid.
3. Vo Thi Sau attacked some French soldiers when she was only 14.
4. Steve Jobs passed away when he was only 56 years old.
