{"id":4783,"date":"2022-09-02T15:28:19","date_gmt":"2022-09-02T13:28:19","guid":{"rendered":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/rovnice-priklad-4-zlomky\/"},"modified":"2022-09-02T15:28:19","modified_gmt":"2022-09-02T13:28:19","slug":"rovnice-priklad-4-zlomky","status":"publish","type":"lesson","link":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/rovnice-priklad-4-zlomky\/","title":{"rendered":"Rovnice &#8211; p\u0159\u00edklad 4 (zlomky)"},"content":{"rendered":"<p><strong>Zad\u00e1n\u00ed:<\/strong> Pro <em><strong>a \u2208 R<\/strong><\/em> je d\u00e1n v\u00fdraz<br \/>$$\\frac{a &#8211; a^{-1}}{a^{0}-a^{2}}$$<br \/><strong>a) Zjednodu\u0161te v\u00fdraz<\/strong><br \/><strong>b) Zjist\u011bte, pro kter\u00e1 re\u00e1ln\u00e1 \u010d\u00edsla a m\u00e1 v\u00fdraz smysl<\/strong><\/p>\n<p><strong>\u0158e\u0161en\u00ed:<\/strong><\/p>\n<p><em>a) Zjednodu\u0161en\u00ed v\u00fdrazu<\/em><br \/>1) Nejprve uprav\u00edme na n\u00e1sleduj\u00edc\u00ed tvar<br \/>$$\\frac{a&nbsp; &#8211;&nbsp;\\frac{1}{a}}{1-a^{2}}$$<br \/>2) D\u00e1le uprav\u00edme \u010ditatele<br \/>$$\\frac{\\frac{a^{2}-1}{a}}{1-a^{2}}$$<br \/>3) Odebereme z \u010ditatele zlomek<br \/>$$\\frac{a^{2} &#8211; 1}{a (1 &#8211;&nbsp;a^{2})}$$<br \/>4) Zbav\u00edme mocnitele rozn\u00e1soben\u00edm<br \/>$$\\frac{(a &#8211; 1)(a + 1)}{a (1 &#8211;&nbsp;a)(1 + a)}$$<br \/>5) Nyn\u00ed ze dvou z\u00e1vorek v \u010ditateli i jmenovateli ud\u011bl\u00e1me jen jednu<br \/>$$\\frac{- (1 &#8211; a)}{a (1 &#8211; a)}$$<br \/>6) V posledn\u00edm kroku uprav\u00edme zlomek tak, aby v n\u011bm nebyly z\u00e1vorky<br \/>$$-\\frac{1}{a}$$<br \/><em>b) Re\u00e1ln\u00e1 \u010d\u00edsla, pro kter\u00e1 m\u00e1 v\u00fdraz smysl<\/em><br \/>V\u00fdraz a m\u00e1 smysl pro a\u22600; a\u22601;&nbsp;a\u2260-1<\/p>\n<p>\u010casov\u00e1 n\u00e1ro\u010dnost: 5 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-4783","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 4 (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-4-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 4 (zlomky) | Studijni-svet.cz\" \/>\n<meta property=\"og:description\" content=\"Zad\u00e1n\u00ed: Pro a \u2208 R je d\u00e1n v\u00fdraz$$frac{a &#8211; a^{-1}}{a^{0}-a^{2}}$$a) Zjednodu\u0161te v\u00fdrazb) Zjist\u011bte, pro kter\u00e1 re\u00e1ln\u00e1 \u010d\u00edsla a m\u00e1 v\u00fdraz smysl \u0158e\u0161en\u00ed: a) Zjednodu\u0161en\u00ed v\u00fdrazu1) Nejprve uprav\u00edme na n\u00e1sleduj\u00edc\u00ed tvar$$frac{a&nbsp; &#8211;&nbsp;frac{1}{a}}{1-a^{2}}$$2) D\u00e1le uprav\u00edme \u010ditatele$$frac{frac{a^{2}-1}{a}}{1-a^{2}}$$3) Odebereme z \u010ditatele zlomek$$frac{a^{2} &#8211; 1}{a (1 &#8211;&nbsp;a^{2})}$$4) Zbav\u00edme mocnitele rozn\u00e1soben\u00edm$$frac{(a &#8211; 1)(a + 1)}{a (1 &#8211;&nbsp;a)(1 + a)}$$5) Nyn\u00ed ze ... 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