Đáp án:

$b. x = \frac{-45}{58}$

$d. x = \frac{18}{7}$

$k. \frac{27}{2(x-1)}$

$n. x = \frac{3}{4}$

Giải thích các bước giải:

$b. ( \frac{-2}{3}x - \frac{3}{5} )( \frac{3}{-2} - \frac{10}{3} ) = \frac{2}{5}$

⇔ $( \frac{-2}{3}x - \frac{3}{5} )( \frac{3×3-10×(-2)}{-2×3} ) = \frac{2}{5}$

⇔ $( \frac{-2}{3}x - \frac{3}{5} ).\frac{9+20}{-6} = \frac{2}{5}$

⇔ $( \frac{2}{3}x + \frac{3}{5} ).\frac{29}{6} = \frac{2}{5}$

⇔ $\frac{2}{3}x + \frac{3}{5} = \frac{2}{5} : \frac{29}{6}$

⇔ $\frac{2}{3}x + \frac{3}{5} = \frac{2}{5}.\frac{6}{29}$

⇔ $\frac{2}{3}x + \frac{3}{5} = \frac{12}{145}$

⇔ $\frac{2}{3}x = \frac{12}{145} - \frac{3}{5}$

⇔ $\frac{2}{3}x = \frac{12}{145} - \frac{3×29}{5×29}$

⇔ $\frac{2}{3}x = \frac{12}{145} - \frac{87}{145}$

⇔ $\frac{2}{3}x = \frac{-75}{145}$

⇔ $\frac{2}{3}x = \frac{-15}{29}$

⇔ $x = \frac{-15}{29} : \frac{2}{3}$

⇔ $x = \frac{-15}{29}.\frac{3}{2}$

⇔ $x = \frac{-45}{58}$

$d. \frac{2x-3}{3} + \frac{-3}{2} = \frac{5-3x}{6} - \frac{1}{3}$

⇔ $\frac{4x-6}{6} - \frac{9}{6} = \frac{5-3x}{6} - \frac{2}{6}$

⇔ $\frac{4x-15}{6} = \frac{3-3x}{6}$

⇔ $4x - 15 = 3 - 3x$

⇔ $4x + 3x = 3 + 15$

⇔ $7x = 18$

⇔ $x = \frac{18}{7}$

$k. \frac{13}{x-1} + \frac{5}{2x-2} - \frac{6}{3x-3}$ $( x \ne 1 )$

$= \frac{13}{x-1} + \frac{5}{2(x-1)} - \frac{6}{3(x-1)}$

$= \frac{26}{2(x-1)} + \frac{5}{2(x-1)} - \frac{2}{x-1}$

$= \frac{31}{2(x-1)} - \frac{4}{2(x-1)}$

$= \frac{27}{2(x-1)}$

$n. ( \frac{3}{2} - \frac{5}{11} - \frac{3}{13} )( 2x - 2 ) = ( - \frac{3}{4} + \frac{5}{22} + \frac{3}{26} )$

⇔ $( \frac{3}{2} - \frac{5}{11} - \frac{3}{13} )( 2x - 2 ) = - \frac{1}{2}( \frac{3}{2} - \frac{5}{11} - \frac{3}{13} )$

⇔ $2x - 2 = - \frac{1}{2}$

⇔ $4x - 4 = -1$

⇔ $4x = - 1 + 4$

⇔ $4x = 3$

⇔ $x = \frac{3}{4}$