{"id":4785,"date":"2022-09-02T15:32:15","date_gmt":"2022-09-02T13:32:15","guid":{"rendered":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/rovnice-priklad-6-zlomky\/"},"modified":"2022-09-02T15:32:15","modified_gmt":"2022-09-02T13:32:15","slug":"rovnice-priklad-6-zlomky","status":"publish","type":"lesson","link":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/rovnice-priklad-6-zlomky\/","title":{"rendered":"Rovnice &#8211; p\u0159\u00edklad 6 (zlomky)"},"content":{"rendered":"<p><strong>Zad\u00e1n\u00ed:<\/strong> V oboru <em><strong>R<\/strong><\/em> \u0159e\u0161te rovnici:<\/p>\n<p>$$\\frac{x + 10}{x}+\\frac{100}{10x &#8211; x^{2}}=\\frac{x + 20}{x &#8211; 10}$$<\/p>\n<p><strong>\u0158e\u0161en\u00ed:<\/strong><\/p>\n<p>1) U 2. zlomku ve jmenovateli vytkneme x, aby se n\u00e1m s n\u00edm l\u00e9pe pracovalo<br \/>$$\\frac{x + 10}{x}+\\frac{100}{x(10 &#8211; x)}=\\frac{x + 20}{x &#8211; 10}$$<br \/>2) Je\u0161t\u011b si u 2. zlomku vym\u011bn\u00edme pozice \u010d\u00edsla a nezn\u00e1m\u00e9<br \/>$$\\frac{x + 10}{x}-\\frac{100}{x(x &#8211; 10)}=\\frac{x + 20}{x &#8211; 10}$$<br \/>3) Zbav\u00edme se zlomk\u016f, spole\u010dn\u00fd jmenovatel je x(x-10);&nbsp; ve zlomc\u00edch, kde n\u011bjak\u00e1 \u010d\u00e1st spole\u010dn\u00e9ho jmenovatele chyb\u00ed, mus\u00edme chyb\u011bj\u00edc\u00ed \u010d\u00e1st\u00ed ve jmenovateli vyn\u00e1sobit \u010ditatele dan\u00e9ho zlomku<br \/>$$(x + 10)(x &#8211; 10) &#8211; 100 = x(x + 20)$$<br \/>4) Nyn\u00ed se rozn\u00e1soben\u00edm zbav\u00edme z\u00e1vorek<br \/>$$x^{2} &#8211; 100 &#8211; 100 = x^{2} + 20x$$<br \/>5) Na jedn\u00e9 stran\u011b si nech\u00e1me nezn\u00e1m\u00e9 a na druh\u00e9 \u010d\u00edsla, x na druhou se n\u00e1m anuluj\u00ed<br \/>$$- 200 = 20x$$<br \/>6) P\u0159epo\u010d\u00edt\u00e1me na 1 x<br \/>$$x = -10$$<\/p>\n<p>\u010casov\u00e1 n\u00e1ro\u010dnost: 5-6 minut<\/p>\n<p>Jedn\u00e1 se o p\u0159\u00edklad z maturitn\u00edho testu.<\/p>\n","protected":false},"comment_status":"open","ping_status":"closed","template":"","class_list":["post-4785","lesson","type-lesson","status-publish","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.5 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Rovnice - p\u0159\u00edklad 6 (zlomky) | Studijni-svet.cz<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/rovnice-priklad-6-zlomky\/\" \/>\n<meta property=\"og:locale\" content=\"cs_CZ\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Rovnice - p\u0159\u00edklad 6 (zlomky) | Studijni-svet.cz\" \/>\n<meta property=\"og:description\" content=\"Zad\u00e1n\u00ed: V oboru R \u0159e\u0161te rovnici: $$frac{x + 10}{x}+frac{100}{10x &#8211; x^{2}}=frac{x + 20}{x &#8211; 10}$$ \u0158e\u0161en\u00ed: 1) U 2. zlomku ve jmenovateli vytkneme x, aby se n\u00e1m s n\u00edm l\u00e9pe pracovalo$$frac{x + 10}{x}+frac{100}{x(10 &#8211; x)}=frac{x + 20}{x &#8211; 10}$$2) Je\u0161t\u011b si u 2. zlomku vym\u011bn\u00edme pozice \u010d\u00edsla a nezn\u00e1m\u00e9$$frac{x + 10}{x}-frac{100}{x(x &#8211; 10)}=frac{x + 20}{x ... 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