a)
[tex]\frac{x}{1.2}=\frac{(2.5-1\frac{2}{3})^2}{\frac{5}{24}}\\
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\frac{x}{\frac{12}{10}}=\frac{(\frac{25}{10}-\frac{5}{3})^2}{\frac{5}{24}}\\
[/tex]
Aducem la acelasi numitor, acesta fiind 30
[tex]\frac{10}{12}x=\left(\frac{3\cdot25-10\cdot5}{30}\right)^2\cdot\frac{24}{5}\\
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\frac{10}{12}x=\left(\frac{75-50}{30}\right)^2\cdot\frac{24}{5}\\
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\frac{10}{12}x=\frac{25^2}{30^2}\cdot\frac{24}{5}\\
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\frac{10}{12}x=\frac{625}{900}\cdot\frac{24}{5}[/tex]
Simplificam 900 si 24 prin 4, si 625 si 5 prin 5:
[tex]\frac{10}{12}x=\frac{125\cdot6}{225}\\
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10x\cdot225=12\cdot125\cdot6\\
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2250x=9000\\
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x=\frac{9000}{2250}=4[/tex]
b)
[tex]\frac{8\frac{8}{15}\left[\frac{1}{5}+x\left(1\frac{1}{3}-1\frac{1}{5}\right)\right]\cdot1\frac{2}{3}}{2,1(3)}=\frac{16^8}{8^{10}}=\frac{2^8\cdot8^8}{8^8\cdot8^2}=\frac{2^3\cdot2^3\cdot2^2}{8^2}=2^2\\
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\frac{\frac{128}{15}\left[\frac{1}{5}+x\left(\frac{4}{3}-\frac{6}{5}\right)\right]\cdot\frac{5}{3}}{\frac{213-21}{90}}=4\\
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\frac{128}{15}\cdot(\frac{1}{5}+\frac{20-18}{15}x)\cdot\frac{5}{3}\cdot\frac{90}{192}=4\\
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\frac{128\cdot5\cdot90}{15\cdot3\cdot192}\cdot\frac{3+2}{15}x=4\\[/tex]
[tex]\frac{57600}{8640}\cdot\frac{5}{15}x=4\\
[/tex]
Prin simplificari:
[tex]\frac{20}{3}\cdot\frac{5}{15}x=4\\
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100x=4\cdot45\\
x=\frac{180}{100}=1,8[/tex]