[tex] \dfrac{ x+3 }{5}^{ \times 42} + \dfrac{x + 5}{6}^{ \times 35} + \dfrac{x + 7}{7}^{ \times 30} = 6 \\ \\ \\ n.c. = 5 \times 6 \times 7 = 210 \\ \\ 210 \div 5 = 42 \\ \\ 210 \div 6 = 35 \\ \\ 210 \div 7 = 30 \\ \\ \\ \dfrac{42x + 126}{210} + \dfrac{35x +175 }{210} + \dfrac{30x + 210}{210} = \dfrac{6}{1} \\ \\ \\ \dfrac{42x + 126 + 35x + 175 + 30x + 210}{210} = 6 \\ \\ \\ \dfrac{107x + 511}{210} = \dfrac{6}{1} \\ \\ \\ 210 \times 6 = 1260 \\ \\ 1 \times (107x + 511) = 1260 \\ \\ \\ 107x + 511 = 1260 \div 1 \\ \\ 107x + 511 = 1260 \\ \\ 107x = 1260 - 511 \\ \\ 107x = 749 \\ \\ x = 749 \div 107 \\ \\ x = 7[/tex]
