Răspuns:
[tex]a) \frac{x}{2} = \frac{6}{4} \\ x \times 4 = 6 \times 2 \\ 4x = 12 \\ x = 12 \div 4 \\ x = 3[/tex]
[tex]b) \frac{x}{3} = \frac{10}{2} \\ x \times 2 = 10 \times 3 \\ 2x = 30 \\ x = 30 \div 2 \\ x = 15[/tex]
[tex]c) \frac{x}{5} = \frac{4}{2} \\ 2x = 5 \times 4 \\ 2x = 20 \\ x = 20 \div 2 \\ x = 10[/tex]
[tex]d) \frac{4}{x} = 12 \\ 4 \times 1 = 12 \times x \\ 12x = 4 \\ x = \frac{4}{12} \\ x = \frac{1}{3} [/tex]
[tex]e) \frac{7}{x} = \frac{1}{2} \\ 7 \times 2 = x \times 1 \\ x = 14[/tex]
[tex]f) \frac{0.1}{x} = \frac{1}{5} \\ x \times 1 = 0.1 \times 5 \\ x = \frac{1}{10} \times 5 \\ x = \frac{1}{2} [/tex]
[tex]g) \frac{1}{3} = \frac{x}{27} \\ 1 \times 27 = 3 \times x \\ 3x = 27 \\ x = 27 \div 3 \\ x = 9[/tex]
[tex]h) \frac{2}{3} = \frac{6}{x} \\ 2 \times x = 3 \times 6 \\ 2x = 18 \\ x = 18 \div 2 \\ x = 9[/tex]
[tex]i) \frac{x}{2} = 0.(5) \\ \frac{x}{2} = \frac{5}{9} \\ x \times 9 = 2 \times 5 \\ 9x = 10 \\ x = \frac{10}{9} [/tex]
[tex] \frac{a \times b}{a \times b - 5} = \frac{a \times b + 2}{a \times b} \\ notam \: a \times b \: cu \: x \\ \frac{x}{x - 5} = \frac{x + 2}{x} \\ x \times x = (x - 2)(x - 5) \\ {x}^{2} = {x}^{2} - 5 \times x - 2 \times x - 2 \times ( - 5) \\ {x}^{2} = {x}^{2} - 5x - 2x + 10 \\ {x}^{2} - {x}^{2} + 5x + 2x = 10 \\ 7x = 10 \\ x = \frac{10}{7} \\ a \times b = \frac{10}{7} \\ a = \frac{2}{7} \\ b = 5 \\ sau \: a = 5 \: b = \frac{2}{7} [/tex]
