Question

VA ROG DIN SUFLET SA MA AJUTAȚI , LA EXERCIȚIILE 1 , 2 , 3 , 4 , RAPID VA ROG !

Answer 1

$1) \frac{12x - 5y}{3x} = \frac{2}{3}$

$3(12x - 5y) = 2 \times 3x$

$36x - 15y = 6x$

$36x - 6x = 15y$

$30x = 15y$

$x = \frac{15y}{30}$

$x = \frac{y}{2}$

$2x = y$

$\frac{2x}{y} = 1 \: | \div 2$

$\frac{x}{y} = \frac{1}{2}$

$\frac{ {x}^{2} + xy }{ {y}^{2} } = \frac{x(x + y)}{ {y}^{2} }$

$\frac{ \frac{y}{2}( \frac{y}{2} + y) }{ {y}^{2} } \: | \times 2$

$= \frac{y(y + 2y)}{ {y}^{2} }$

$= \frac{y + 2y}{y}$

$= \frac{3y}{y}$

$= 3$

$2) \frac{x - 1}{1 + \frac{1}{2} } = \frac{ \frac{7}{3} - 1}{3 - \frac{3}{2} }$

$\frac{x - 1}{ \frac{2}{2} + \frac{1}{2} } = \frac{ \frac{7}{3} - \frac{3}{3} }{ \frac{6}{2} - \frac{3}{2} }$

$\frac{x - 1}{ \frac{2 + 1}{2} } = \frac{ \frac{7 - 3}{3} }{ \frac{6 - 3}{2} }$

$\frac{x - 1}{ \frac{3}{2} } = \frac{ \frac{4}{3} }{ \frac{3}{2} }$

$x - 1 = \frac{4}{3} \: | \times 3$

$3x - 3 = 4$

$3x = 4 + 3$

$3x = 7$

$x = \frac{7}{3}$

$b) \frac{2x + 1}{4x + 3} = \frac{1}{3}$

$3(2x + 1) = 4x + 3$

$6x + 3 = 4x + 3$

$6x - 4x = 0$

$2x = 0$

$x = \frac{0}{2}$

$x = 0$

$3)x - nr. \: de \: pagini \: al \: cartii$

$\frac{30}{100} \times x = \frac{30x}{100} = \frac{3x}{10}$

$\frac{3x}{10} + 140 = x \: | \times 10$

$3x + 1400 = 10x$

$3x - 10x = - 1400$

$- 7x = - 1400 \: | \div ( - 7)$

$x = 200$

$4) \frac{a}{b} = \frac{2}{3}$

$c.m.m.m.c = 36$

$\frac{12}{18} = \frac{2}{3}$

$numerele \: sunt \: 12 \: si \: 18.$