4x+3y:5x-2y=?
X si y direct proportionale cu 5 si 9
SmartGIRL12:
ai scris bine prima ec?
Trebuia sa folosesti paranteze.
adica trebuia sa scrie asa (4x+3y):(5x-2y) ?
Da, asa e corect.
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[tex]\displaystyle\\ \frac{x}{5} = \frac{y}{9} ~~~ \Longleftrightarrow ~~~\boxed{\frac{x}{y} = \frac{5}{9}}\\\\ \frac{4x+3y}{5x-2y}=~~~\text{Simplificam fortat fractia cu } ~\boxed{y}\\\\\\ =\frac{4\cdot \frac{x}{y} +3\cdot \frac{y}{y} }{5\cdot\frac{x}{y} -2\cdot\frac{y}{y}}=\frac{4\cdot \frac{x}{y} +3 }{5\cdot\frac{x}{y} -2}= \frac{4\cdot \frac{5}{9} +3 }{5\cdot\frac{5}{9} -2}= \frac{\frac{20}{9} +3 }{\frac{25}{9} -2}= [/tex]
[tex]\displaystyle\\ = \frac{\frac{20+3\cdot9}{9} }{\frac{25-2\cdot 9}{9}}=\frac{20+3\cdot9}{9}\cdot \frac{9}{25-2\cdot 9}=\frac{20+3\cdot9}{25-2\cdot 9}=\frac{20+27}{25-18}= \boxed{\frac{47}{7}} [/tex]
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