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HomeLớp 8Toán lớp 8 - Sách Kết nối tri thứcBài 22. Tính chất cơ bản của phân thức đại sốBài tập nâng cao
{"common":{"save":0,"post_id":"6599","level":3,"total":10,"point":10,"point_extra":0},"segment":[{"id":"6443","post_id":"6599","mon_id":"1158921","chapter_id":"1158930","question":"<p>Giá tr\u1ecb l\u1edbn nh\u1ea5t c\u1ee7a phân th\u1ee9c <span class=\"math-tex\">$\\dfrac{1}{x^2+2x+3}$<\/span> là:<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$\\dfrac{1}{3}$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$\\dfrac{1}{2}$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$\\dfrac{-1}{2}$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$\\dfrac{1}{5}$<\/span>"],"correct":"2","level":"3","hint":"","answer":"<p>Ta có: <span class=\"math-tex\">$x^2+2x+3=(x+1)^2+2\\ge 2$<\/span><\/p><p>Suy ra <span class=\"math-tex\">$\\dfrac{1}{x^2+2x+3}\\le \\dfrac{1}{2}$<\/span> <\/p><p>Do \u0111ó giá tr\u1ecb l\u1edbn nh\u1ea5t c\u1ee7a phân th\u1ee9c <span class=\"math-tex\">$\\dfrac{1}{x^2+2x+3}$<\/span> là <span class=\"math-tex\">$\\dfrac{1}{2}$<\/span> \u0111\u1ea1t \u0111\u01b0\u1ee3c khi <span class=\"math-tex\">$(x+1)^2=0\\Leftrightarrow x=-1$<\/span><\/p><p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>B.<\/strong> <span class=\"math-tex\">$\\dfrac{1}{2}$<\/span><\/span><\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"131","test":"0","date":"2023-08-25 22:21:40","option_type":"math","len":0},{"id":"6444","post_id":"6599","mon_id":"1158921","chapter_id":"1158930","question":"<p>Tìm các giá tr\u1ecb nguyên c\u1ee7a x \u0111\u1ec3 phân th\u1ee9c <span class=\"math-tex\">$\\dfrac{-5}{x+3}$<\/span> có giá tr\u1ecb nguyên.<\/p>","options":["<strong>A.<\/strong> x ∈ { –8 ; –4 ; –2 ; 2 }","<strong>B.<\/strong> x ∈ { –5 ; –4 ; –3 ; 0 }","<strong>C.<\/strong> x ∈ { –6 ; –4 ; –2 ; 0 }","<strong>D.<\/strong> x ∈ { –7 ; –5 ; –3 ; 1 }"],"correct":"1","level":"3","hint":"","answer":"<p>\u0110\u1ec3 phân th\u1ee9c <span class=\"math-tex\">$\\dfrac{-5}{x+3}$<\/span> có giá tr\u1ecb nguyên thì <span class=\"math-tex\">$-5\\space\\vdots \\space (x+3)$<\/span><\/p><p>Suy ra <span class=\"math-tex\">$(x+3)\\in \u01af(-5)$<\/span><\/p><p>Ta có: <span class=\"math-tex\">$\u01af(-5)=\\{ -5; -1 ; 1; 5\\}$<\/span><\/p><p>+ V\u1edbi x + 3 = –5 thì x = <span style=\"color:#16a085;\">–8<\/span> (nh\u1eadn)<\/p><p>+ V\u1edbi x + 3 = –1 thì x = <span style=\"color:#16a085;\">–4<\/span> (nh\u1eadn)<\/p><p>+ V\u1edbi x + 3 = 1 thì x = <span style=\"color:#16a085;\">–2<\/span> (nh\u1eadn)<\/p><p>+ V\u1edbi x + 3 = 5 thì x = <span style=\"color:#16a085;\">2<\/span> (nh\u1eadn)<\/p><p>V\u1eady <span style=\"color:#16a085;\">x ∈ { –8 ; –4 ; –2 ; 2 }<\/span> thì phân th\u1ee9c <span class=\"math-tex\">$\\dfrac{-5}{x+3}$<\/span> có giá tr\u1ecb nguyên.<\/p><p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>A.<\/strong> x ∈ { –8 ; –4 ; –2 ; 2 }<\/span><\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"131","test":"0","date":"2023-08-25 22:24:23","option_type":"txt","len":2},{"id":"6449","post_id":"6599","mon_id":"1158921","chapter_id":"1158930","question":"<p>Tìm m\u1eabu th\u1ee9c chung c\u1ee7a các phân th\u1ee9c sau:<\/p><p><span class=\"math-tex\">$\\dfrac{x-1}{x+3}$<\/span> ; <span class=\"math-tex\">$\\dfrac{x^2}{x^3+27}$<\/span> ; <span class=\"math-tex\">$\\dfrac{-2}{x^2-9}$<\/span><\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$(x+3)^2(x^2-3x+9)$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$(x+3)(x-3)(x^2-3x+9)$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$(x+3)(x^2-9)(x^2-3x+9)$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$(x+3)(x-3)(x^3+27)$<\/span>"],"correct":"2","level":"3","hint":"","answer":"<p>Các m\u1eabu th\u1ee9c riêng là:<\/p><p><span style=\"color:#2980b9;\">x + 3<\/span><\/p><p>x³ + 27 = (<span style=\"color:#2980b9;\">x + 3<\/span>)(<span style=\"color:#8e44ad;\">x² – 3x + 9<\/span>)<\/p><p>x² – 9 = (<span style=\"color:#2980b9;\">x + 3)<\/span>( <span style=\"color:#f39c12;\">x – 3<\/span>)<\/p><p>Do \u0111ó m\u1eabu th\u1ee9c chung là <span style=\"color:#16a085;\"><span class=\"math-tex\">$(x+3)(x-3)(x^2-3x+9)$<\/span><\/span><\/p><p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>B.<\/strong> <span class=\"math-tex\">$(x+3)(x-3)(x^2-3x+9)$<\/span><\/span><\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"131","test":"0","date":"2023-08-25 22:45:23","option_type":"math","len":0}]}