[tex]1) \frac{12x - 5y}{3x} = \frac{2}{3} [/tex]
[tex]3(12x - 5y) = 2 \times 3x[/tex]
[tex]36x - 15y = 6x[/tex]
[tex]36x - 6x = 15y[/tex]
[tex]30x = 15y[/tex]
[tex]x = \frac{15y}{30} [/tex]
[tex]x = \frac{y}{2} [/tex]
[tex]2x = y[/tex]
[tex] \frac{2x}{y} = 1 \: | \div 2[/tex]
[tex] \frac{x}{y} = \frac{1}{2} [/tex]
[tex] \frac{ {x}^{2} + xy }{ {y}^{2} } = \frac{x(x + y)}{ {y}^{2} } [/tex]
[tex] \frac{ \frac{y}{2}( \frac{y}{2} + y) }{ {y}^{2} } \: | \times 2[/tex]
[tex] = \frac{y(y + 2y)}{ {y}^{2} } [/tex]
[tex] = \frac{y + 2y}{y} [/tex]
[tex] = \frac{3y}{y} [/tex]
[tex] = 3[/tex]
[tex]2) \frac{x - 1}{1 + \frac{1}{2} } = \frac{ \frac{7}{3} - 1}{3 - \frac{3}{2} } [/tex]
[tex] \frac{x - 1}{ \frac{2}{2} + \frac{1}{2} } = \frac{ \frac{7}{3} - \frac{3}{3} }{ \frac{6}{2} - \frac{3}{2} } [/tex]
[tex] \frac{x - 1}{ \frac{2 + 1}{2} } = \frac{ \frac{7 - 3}{3} }{ \frac{6 - 3}{2} } [/tex]
[tex] \frac{x - 1}{ \frac{3}{2} } = \frac{ \frac{4}{3} }{ \frac{3}{2} } [/tex]
[tex]x - 1 = \frac{4}{3} \: | \times 3[/tex]
[tex]3x - 3 = 4[/tex]
[tex]3x = 4 + 3[/tex]
[tex]3x = 7[/tex]
[tex]x = \frac{7}{3} [/tex]
[tex]b) \frac{2x + 1}{4x + 3} = \frac{1}{3} [/tex]
[tex]3(2x + 1) = 4x + 3[/tex]
[tex]6x + 3 = 4x + 3[/tex]
[tex]6x - 4x = 0[/tex]
[tex]2x = 0[/tex]
[tex]x = \frac{0}{2} [/tex]
[tex]x = 0[/tex]
[tex]3)x - nr. \: de \: pagini \: al \: cartii[/tex]
[tex] \frac{30}{100} \times x = \frac{30x}{100} = \frac{3x}{10} [/tex]
[tex] \frac{3x}{10} + 140 = x \: | \times 10[/tex]
[tex]3x + 1400 = 10x[/tex]
[tex]3x - 10x = - 1400[/tex]
[tex] - 7x = - 1400 \: | \div ( - 7)[/tex]
[tex]x = 200[/tex]
[tex]4) \frac{a}{b} = \frac{2}{3} [/tex]
[tex]c.m.m.m.c = 36[/tex]
[tex] \frac{12}{18} = \frac{2}{3} [/tex]
[tex]numerele \: sunt \: 12 \: si \: 18.[/tex]
