[tex]\displaystyle\bf\\\frac{a+b}{a-b}=\frac{5}{3}\\\\\textbf{Simplificam FORTAT fractia cu b.}\\\\\frac{~~\dfrac{a+b}{b}~~}{\dfrac{a-b}{b}}=\frac{5}{3}\\\\\\\frac{~~\dfrac{a}{b}+\dfrac{b}{b}~~}{\dfrac{a}{b}-\dfrac{b}{b}}=\frac{5}{3}\\\\\\\frac{~~\dfrac{a}{b}+1~~}{\dfrac{a}{b}-1}=\frac{5}{3}[/tex]
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[tex]\displaystyle\bf\\\textbf{Produsul mezilor = produsul extremilor}\\\\5\Big(\dfrac{a}{b}-1\Big)=3\Big(\dfrac{a}{b}+1\Big)\\\\5\times\frac{a}{b}-5=3\times\dfrac{a}{b}+3\\\\5\times\frac{a}{b}-3\times\dfrac{a}{b}=3+5\\\\2\times\frac{a}{b}=8\\\\\frac{a}{b}=\frac{8}{2}\\\\\boxed{\bf\frac{a}{b}=4}[/tex]
