Question

Решите уравнение и сделайте проверку 1/х+3/2 2/5х=3/4,1/x-2/4 2/3x=2/7,6/3 1/3x+1/x=2/5

Answer 1

1) 3

2) 2

3) 7

Пошаговое объяснение:

Уравнение 1.

$\tt\displaystyle \frac{1}{x} +\frac{3}{2\frac{2}{5}x } =\frac{3}{4}\\\\\\\frac{1}{x} +\frac{3}{\frac{12}{5}x } =\frac{3}{4} \\\\\\\frac{1}{x} +\frac{5}{4x } =\frac{3}{4}\ |*4x \\\\\\4+5=3x\\\\3x=9\\\\x=3$

Проверка.

$\tt\displaystyle \frac{1}{3} +\frac{3}{2\frac{2}{5}*3 } =\frac{3}{4}\\\\\\\frac{1}{3} +\frac{3}{\frac{12}{5}*3 } =\frac{3}{4}\\\\\\\frac{1}{3} +\frac{1}{\frac{12}{5} } =\frac{3}{4}\\\\\\\frac{1}{3} +\frac{5}{12} =\frac{3}{4}\\\\\\\frac{1*4}{3*4} +\frac{5}{12 } =\frac{3}{4}\\\\\\\frac{4}{12} +\frac{5}{12 } =\frac{3}{4}\\\\\\\frac{4+5}{12}=\frac{3}{4}\\\\\\\frac{9}{12} =\frac{3}{4}\\\\\\\frac{9:3}{12:3}=\frac{3}{4}\\\\\\\frac{3}{4} =\frac{3}{4}$

Второе уравнение.

$\tt\displaystyle \frac{1}{x} -\frac{2}{4\frac{2}{3}x } =\frac{2}{7} \\\\\\\\\frac{1}{x} -\frac{2}{\frac{14}{3}x } =\frac{2}{7}\\\\\\\frac{1}{x} -\frac{3}{7x} =\frac{2}{7}\ |*7x\\\\\\7-3=2x\\\\2x=4\\\\x=2$

Проверка.

$\tt\displaystyle \frac{1}{2} -\frac{2}{4\frac{2}{3}*2 } =\frac{2}{7}\\\\\\\frac{1}{2} -\frac{2}{\frac{14}{3}*2 } =\frac{2}{7}\\\\\\\frac{1}{2} -\frac{1}{\frac{14}{3} } =\frac{2}{7}\\\\\\\frac{1*7}{2*7}-\frac{3}{14}=\frac{2*2}{7*2} \\\\\\\frac{7}{14}-\frac{3}{14}=\frac{4}{14} \\\\\\ \frac{4}{14}=\frac{4}{14}$

Третье уравнение.

$\tt\displaystyle \frac{6}{3\frac{1}{3}x } +\frac{1}{x} =\frac{2}{5} \\\\\\ \frac{6}{\frac{10}{3}x } +\frac{1}{x} =\frac{2}{5}\\\\\\ \frac{9}{5x } +\frac{1}{x} =\frac{2}{5}\ |*5x\\\\\\9+5=2x\\\\2x=14\\\\x=7$

Проверка.

$\tt\displaystyle \frac{6}{3\frac{1}{3}*7 } +\frac{1}{7} =\frac{2}{5}\\\\\\ \frac{6}{\frac{10}{3}*7 } +\frac{1}{7} =\frac{2}{5}\\\\\\\frac{6}{\frac{10*7}{3}} +\frac{1}{7} =\frac{2}{5}\\\\\\\frac{9}{35} +\frac{1*5}{7*5} =\frac{2*7}{5*7}\\\\\\\frac{9}{35} +\frac{5}{35} =\frac{14}{35}\\\\\\\frac{14}{35}=\frac{14}{35}$

Примечания:

3 : 12x/5 = 3 * 5/12x = 5/4x

2 : 14x/3 = 2 * 3/14x = 3/7x

6 : 10x/3 = 6 * 3/10x = 9/5x

6 : (10 * 7)/3 = 6 * 3/(10 * 7) = 9/35