\(-\frac{2,6}{x}=-\frac{12}{42}\)

\(-2,6\cdot42=-12\cdot x\)

\(\frac{109,2}{12}=x\Rightarrow x=9,1\)

a)\(\) Ta có : x / 3,15  =  0,15 / 7,2

            (=)  x = 0,15 . 3,15 / 7,2   

                     = 21 / 320

b)    Ta có : -2,6 / x = -12 / 42

             (=) x = -2,6 . 42 / -12

                     = 91 / 10                                                                                 

\(a.\) \(\frac{x}{3.15}\) \(=\) \(\frac{0.15}{7.2}\) 

<=> \(x=\) \(\frac{0.15\cdot3.15}{7.2}\) 

<=>\(x=0.065625\)

\(b.\) \(\frac{-2.6}{x-11}=\frac{-12}{42}\) 

<=>\(x-11=\frac{-2.6\cdot-12}{42}\)

<=>\(x-11=0.742857142\)

<=>\(x=11.74285714\)

\(3\frac{4}{5}:2x=0,25:2\frac{2}{3}\)

\(\Leftrightarrow\frac{19}{5}:2x=0,25:\frac{8}{3}\)

\(\Leftrightarrow\frac{19}{5}:2x=0,25\cdot\frac{3}{8}\)

\(\Leftrightarrow\frac{19}{5}:2x=\frac{3}{32}\)

\(\Leftrightarrow2x=\frac{19}{5}:\frac{3}{32}=\frac{19}{5}\cdot\frac{32}{3}=\frac{608}{15}\)

\(\Leftrightarrow x=\frac{608}{15}:2=\frac{608}{30}=\frac{304}{15}\)

\(\frac{-2,6}{12}=\frac{x}{-42}\Leftrightarrow x=\frac{\left(-2,6\right)\left(-42\right)}{12}=9,1\)

\(\frac{1,4}{-5}=\frac{2,1}{x}\Leftrightarrow x=\frac{2,1.\left(-5\right)}{1,4}=-7,5\)

\(\frac{3}{x-1}=\frac{21}{16}\Leftrightarrow x-1=\frac{3.16}{21}=\frac{16}{7};x=\frac{23}{7}\)

\(\frac{1,2}{30}=\frac{3x+4}{50}\Leftrightarrow3x+4=\frac{50.1,2}{30}=2;3x=-1;x=-\frac{1}{3}\)

a) \(\frac{-2,6}{12}=\frac{x}{42}\)

\(x=\frac{-2,6.\left(-42\right)}{12}=9,1\)

b) \(\frac{1.4}{-5}=\frac{2,1}{x}\)

\(x=\frac{-5.2,1}{1,4}=-7,5\)

c) \(\frac{3}{x-1}=\frac{21}{16}\)

\(x-1=\frac{3.16}{21}=\frac{16}{7}\)

\(x=\frac{16}{7}+1=\frac{23}{7}\)

d) \(\frac{1,2}{30}=\frac{3x+4}{50}\)

\(3x+4=\frac{12.50}{30}=20\)

\(3x=20-4=16\)

\(x=16:3=\frac{16}{3}\)

\(a,\frac{-2,6}{x}=-\frac{12}{42}\)

\(\Leftrightarrow\left(-2,6\right).42=-12x\)

\(\Leftrightarrow-12x=-\frac{546}{5}\)

\(\Leftrightarrow x=\frac{91}{10}\)

\(b,\frac{x^2}{6}=\frac{24}{25}\)

\(\Leftrightarrow25x^2=24.6\)

\(\Leftrightarrow25x^2=144\)

\(\Leftrightarrow x^2=\frac{144}{25}\)

\(\Leftrightarrow x=\frac{12}{5}\)

Bài 1:

a) Áp dụng tính chất dãy tỉ số bằng nhau ta có:

\(\frac{a}{b}=\frac{c}{d}=\frac{a+c}{b+d}=\frac{a-c}{b-d}\)

Vậy \(\frac{a+c}{b+d}=\frac{a-c}{b-d}\)

b) Ta có: \(\frac{a}{b}=\frac{c}{d}\Leftrightarrow\frac{a}{c}=\frac{b}{d}\Leftrightarrow\frac{2a}{2c}=\frac{3b}{3d}\)

Áp dụng tính chất dãy tỉ số bằng nhau ta có:

\(\frac{2a}{2c}=\frac{3b}{3d}=\frac{2a+3b}{2c+3d}=\frac{2a-3b}{2c-3d}\)

Vì \(\frac{2a+3b}{2c+3d}=\frac{2a-3b}{2c-3d}\)nên \(\frac{2a+3b}{2a-3b}=\frac{2c+3d}{2c-3d}\left(ĐPCM\right)\)

Bài 2:

\(\text{a)}\frac{-2,6}{x}=\frac{-12}{42}\)

\(\Rightarrow-12.x=-2,6.42\)

\(\Rightarrow-12.x=-109,2\)

\(\Rightarrow x=\frac{-109,2}{-12}=9,1\)

\(\text{b)}\frac{x^2}{6}=\frac{24}{25}\)

\(\Rightarrow x^2.25=6.24\)

\(\Rightarrow x^2.25=144\)

\(\Rightarrow x^2=\frac{144}{25}\)

\(\Rightarrow x=\pm\sqrt{\frac{144}{25}}=\pm\frac{12}{5}\)

Ta có: \(\frac{x-2}{12}+\frac{x-2}{20}+\frac{x-2}{30}+\frac{x-2}{42}=42^5:\left(2^3\cdot21^6\right)\)

\(\Leftrightarrow\left(x-2\right)\left(\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}\right)=\frac{2^5\cdot21^5}{2^3\cdot21^5\cdot21}\)

\(\Leftrightarrow\left(x-2\right)\cdot\frac{4}{21}=\frac{4}{21}\)

\(\Leftrightarrow x-2=1\)

hay x=3

Vậy: x=3

\(x\left(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}\right)=\frac{4034}{5}\)

\(x.\frac{2}{5}=\frac{4034}{5}\)

\(x=\frac{4034}{5}:\frac{2}{5}\)

\(x=\frac{4034}{5}.\frac{5}{2}\)

x = 2017