\(\dfrac{2}{5}\) x y : \(\dfrac{7}{4}\) = \(\dfrac{7}{8}\)

\(\dfrac{2}{5}\) x y = \(\dfrac{7}{8}\) x \(\dfrac{7}{4}\)

 \(\dfrac{2}{5}\) x y = \(\dfrac{49}{32}\)

         y = \(\dfrac{49}{32}\) : \(\dfrac{2}{5}\)

         y = \(\dfrac{245}{64}\)

2\(\dfrac{2}{5}\): y x 1\(\dfrac{1}{4}\) = 2\(\dfrac{3}{5}\)

\(\dfrac{12}{5}\): y x \(\dfrac{5}{4}\) = \(\dfrac{13}{5}\)

\(\dfrac{12}{5}\): y        = \(\dfrac{13}{5}\): \(\dfrac{5}{4}\)

 \(\dfrac{12}{5}\): y = \(\dfrac{52}{25}\)

        y = \(\dfrac{12}{5}\): \(\dfrac{52}{25}\)

        y = \(\dfrac{15}{13}\)

\(\dfrac{12}{5}\) - 1\(\dfrac{2}{5}\) \(\times\) y = 1\(\dfrac{1}{4}\)

 \(\dfrac{12}{5}\) - \(\dfrac{7}{5}\) \(\times\) y  = \(\dfrac{5}{4}\)

           \(\dfrac{7}{5}\) \(\times\) y  = \(\dfrac{12}{5}\) - \(\dfrac{5}{4}\)

            \(\dfrac{7}{5}\) \(\times\) y = \(\dfrac{23}{20}\)

                   y = \(\dfrac{23}{20}\) : \(\dfrac{7}{5}\)

                   y = \(\dfrac{23}{28}\)

=>x/35=y/28=z/32

Áp dụng tính chất của DTSBN, ta được:

\(\dfrac{x}{35}=\dfrac{y}{28}=\dfrac{z}{32}=\dfrac{x-y+z}{35-28+32}=\dfrac{7}{39}\)

=>x=245/39; y=196/39; z=224/39

x/5 = y/4 => 4x = 5y => x = 5y/4   (1)

y/7 = z/8 => 7z = 8y => z = 8y/7    (2)

có: x-y+z=7

từ (1) và (2) => 5y/4 - y + 8y/7 = 7

<=> 39y/28 = 7

=> y = 196/39

=> x = 245/39

=> z = 224/39

Bài 1:

+) \(\dfrac{7}{8}\times y=\dfrac{3}{2}+\dfrac{6}{4}=3\)

\(y=3:\dfrac{7}{8}=\dfrac{24}{7}\)

+) \(\dfrac{1}{y}\times\left(\dfrac{2}{5}+\dfrac{1}{5}\right)=\dfrac{10}{3}\)

\(\dfrac{1}{y}=\dfrac{10}{3}:\dfrac{3}{5}=\dfrac{50}{9}\)

\(y=\dfrac{9}{50}\)

Bài 2:

+) \(=\dfrac{2}{5}\times\left(\dfrac{4}{7}+\dfrac{3}{7}\right)\)

\(=\dfrac{2}{5}\times\dfrac{7}{7}=\dfrac{2}{5}\)

+) \(\dfrac{2}{9}:\dfrac{2}{3}:\dfrac{3}{9}\)

\(\dfrac{2}{9}\times\dfrac{3}{2}\times\dfrac{9}{3}=1\)

viết rứa ai mà biết

Lời giải:

a. $\frac{x}{7}=\frac{6}{21}$

$x=\frac{6}{21}.7$

$x=2$

b.

$\frac{-5}{y}=\frac{20}{28}$

$y=-5:\frac{20}{28}$

$y=-7$

c.

$\frac{-4}{8}=\frac{-7}{y}$

$y=-7:\frac{-4}{8}$

$y=14$

a, \(\dfrac{x}{7}=\dfrac{6}{21}\Leftrightarrow\dfrac{3x}{21}=\dfrac{6}{21}\Rightarrow x=2\)

b, \(\dfrac{-5}{y}=\dfrac{20}{28}\Leftrightarrow\dfrac{20}{-4y}=\dfrac{20}{28}\Leftrightarrow y=-7\)

c, \(\dfrac{-4}{8}=-\dfrac{7}{y}\Rightarrow-4y=-56\Leftrightarrow y=14\)

a) Ta có: \(\dfrac{x}{7}=\dfrac{6}{21}\)

nên \(x=\dfrac{6\cdot7}{21}=\dfrac{42}{21}=2\)

b) Ta có: \(\dfrac{-5}{y}=\dfrac{20}{28}\)

nên \(y=\dfrac{-5\cdot28}{20}=\dfrac{-140}{20}=-7\)

c) Ta có: \(\dfrac{-4}{8}=\dfrac{-7}{y}\)

nên \(y=\dfrac{-7\cdot8}{-4}=\dfrac{-56}{-4}=14\)

`7/2 : y= 3/8 + 5/4`

`=> 7/2 : y= 3/8 +10/8`

`=> 7/2 : y=13/8`

`=> y= 7/2 : 13/8`

`=> y= 7/2 xx 8/13`

`=> y= 28/13`

\(\dfrac{7}{2}:y=\dfrac{3}{8}+\dfrac{5}{4}\)
\(\dfrac{7}{2}:y=\dfrac{13}{8}\)
\(y=\dfrac{7}{2}:\dfrac{13}{8}\)
\(y=\dfrac{7}{2}\times\dfrac{8}{13}\)
\(y=\dfrac{28}{13}\)

\(\dfrac{1}{x-y}+\dfrac{1}{x+y}+\dfrac{2x}{x^2+y^2}+\dfrac{4x^3}{x^4+y^4}+\dfrac{8x^7}{x^8+y^8}=2x\left(\dfrac{1}{x^2-y^2}+\dfrac{1}{x^2+y^2}\right)+\dfrac{4x^3}{x^4+y^4}+\dfrac{8x^7}{x^8+y^8}=4x^3\left(\dfrac{1}{x^4-y^4}+\dfrac{1}{x^4+y^4}\right)+\dfrac{8x^7}{x^8+y^8}=8x^7\left(\dfrac{1}{x^8-x^8}+\dfrac{1}{x^8+y^8}\right)=\dfrac{16x^{15}}{x^{16}-y^{16}}\)

\(=\dfrac{x+y+x-y}{\left(x-y\right)\left(x+y\right)}+\dfrac{2x}{x^2+y^2}+\dfrac{4x^3}{x^4+y^4}+\dfrac{8x^7}{x^8+y^8}\)

\(=\dfrac{2x}{x^2-y^2}+\dfrac{2x}{x^2+y^2}+\dfrac{4x^3}{x^4+y^4}+\dfrac{8x^7}{x^8+y^8}\)

\(=2x\left(\dfrac{1}{x^2-y^2}+\dfrac{1}{x^2+y^2}\right)+\dfrac{4x^3}{x^4+y^4}+\dfrac{8x^7}{x^8+y^8}\)

\(=\dfrac{4x^3}{x^4-y^4}+\dfrac{4x^3}{x^4+y^4}+\dfrac{8x^7}{x^8+y^8}=4x^3\left(\dfrac{1}{x^4-y^4}+\dfrac{1}{x^4+y^4}\right)+\dfrac{8x^7}{x^8+y^8}\)

\(=\dfrac{8x^7}{x^8-y^8}+\dfrac{8x^7}{x^8+y^8}=8x^7\left(\dfrac{1}{x^8-y^8}+\dfrac{1}{x^8+y^8}\right)\)

\(=\dfrac{16x^{15}}{x^{16}-y^{16}}\)

\(a,2\dfrac{2}{5}:y\times1\dfrac{3}{4}=\dfrac{7}{8}\\ \dfrac{12}{5}:y\times\dfrac{7}{4}=\dfrac{7}{8}\\ \dfrac{12}{5}:y=\dfrac{7}{8}:\dfrac{7}{4}\\ \dfrac{12}{5}:y=\dfrac{1}{2}\\ y=\dfrac{12}{5}:\dfrac{1}{2}=\dfrac{24}{5}\\ b,3\dfrac{2}{5}:y:1\dfrac{1}{4}=2\dfrac{3}{5}\\ \dfrac{17}{5}:y:\dfrac{5}{4}=\dfrac{13}{5}\\ y:\dfrac{5}{4}=\dfrac{17}{5}:\dfrac{13}{5}\\ y:\dfrac{5}{4}=\dfrac{17}{13}\\ y=\dfrac{17}{13}\times\dfrac{5}{4}=\dfrac{85}{52}\)

\(c,\dfrac{12}{5}-2\dfrac{2}{5}\times y=1\dfrac{1}{4}\\ \dfrac{12}{5}-\dfrac{12}{5}\times y=\dfrac{5}{4}\\ \dfrac{12}{5}\times y=\dfrac{12}{5}-\dfrac{5}{4}\\ \dfrac{12}{5}\times y=\dfrac{23}{20}\\ y=\dfrac{23}{20}:\dfrac{12}{5}\\ y=\dfrac{23}{48}\)

a, 2\(\dfrac{2}{5}\): y \(\times\)1\(\dfrac{3}{4}\) = \(\dfrac{7}{8}\)

     \(\dfrac{12}{5}\) : y   \(\times\dfrac{7}{4}\)    = \(\dfrac{7}{8}\)

   \(\dfrac{12}{5}\)  : y         = \(\dfrac{7}{8}\) : \(\dfrac{7}{4}\)

          \(\dfrac{12}{5}\) : y        = \(\dfrac{1}{2}\)       

                  y         = \(\dfrac{12}{5}\) : \(\dfrac{1}{2}\)

                  y         =    \(\dfrac{24}{5}\)

b, 3\(\dfrac{2}{5}\): y : 1\(\dfrac{1}{4}\) = 2\(\dfrac{3}{5}\) 

     \(\dfrac{17}{5}\): y: \(\dfrac{5}{4}\)    = \(\dfrac{13}{5}\)

       \(\dfrac{17}{5}\):y         = \(\dfrac{13}{5}\times\dfrac{5}{4}\)

       \(\dfrac{17}{5}\) : y       = \(\dfrac{13}{4}\)

               y        =   \(\dfrac{17}{5}\) : \(\dfrac{13}{4}\)

               y        =  \(\dfrac{68}{65}\)

c, \(\dfrac{12}{5}\) - 2\(\dfrac{2}{5}\)\(\times y\) = 1\(\dfrac{1}{4}\)

     \(\dfrac{12}{5}\) - \(\dfrac{12}{5}\)\(\times\)y = \(\dfrac{5}{4}\)

            \(\dfrac{12}{5}\times y\) =  \(\dfrac{12}{5}\) - \(\dfrac{5}{4}\)

           \(\dfrac{12}{5}\) \(\times\) y =    \(\dfrac{23}{20}\)

                     \(y\)  = \(\dfrac{23}{20}\): \(\dfrac{12}{5}\)

                     y   = \(\dfrac{23}{48}\)

a)      Ta có \(\dfrac{x}{4} = \dfrac{y}{7}\) và x + y = 55

Áp dụng tính chất tỉ lệ thức ta có : \(\dfrac{x}{4} = \dfrac{y}{7} = \dfrac{{x + y}}{{4 + 7}} = \dfrac{{55}}{{11}} = 5\)

\( \Rightarrow \dfrac{x}{4} = 5 \Rightarrow x = 20\)

\( \dfrac{y}{7} = 5 \Rightarrow y = 35\)

Vậy x = 20; y = 35

b)      \(\dfrac{x}{8} = \dfrac{y}{3}\) và x – y = 35

Áp dụng tính chất tỉ lệ thức ta có : \(\dfrac{x}{8} = \dfrac{y}{3} = \dfrac{{x - y}}{{8 - 3}} = \dfrac{{35}}{5} = 7\)

\( \Rightarrow \dfrac{x}{8} = 7\) \( \Rightarrow \) x = 56

Mà x – y = 35 \( \Rightarrow \) y = 56 – 35 = 21

Vậy x = 56 ; y = 21

Bài 2:

\(a,\dfrac{2}{x}=\dfrac{x}{8}\\ \Rightarrow x.x=8.2\\ \Rightarrow x^2=16\\ \Rightarrow x=\pm4\)

\(b,\dfrac{2x-9}{240}=\dfrac{39}{80}\\ \Rightarrow80\left(2x-9\right)=240.39\\ \Rightarrow160x-720=9360\\ \Rightarrow160x=10080\\ \Rightarrow x=63\)

\(c,\dfrac{x-1}{9}=\dfrac{8}{3}\\ \Rightarrow3\left(x-1\right)=8.9\\ \Rightarrow3\left(x-1\right)=72\\ \Rightarrow x-1=24\\ \Rightarrow x=25\)