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Giải:
a) \(\dfrac{-5}{8}=\dfrac{x}{16}\)
\(\Rightarrow x=\dfrac{16.-5}{8}=-10\)
\(\dfrac{3x}{9}=\dfrac{2}{6}\)
\(\Rightarrow3x=\dfrac{2.9}{6}=3\)
\(\Rightarrow x=1\)
b) \(\dfrac{x+3}{15}=\dfrac{1}{3}\)
\(\Rightarrow x+3=\dfrac{1.15}{3}=5\)
\(\Rightarrow x=2\)
\(\dfrac{6}{2x+1}=\dfrac{2}{7}\)
\(\Rightarrow2x+1=\dfrac{6.7}{2}=21\)
\(\Rightarrow x=10\)
c) \(\dfrac{4}{x-6}=\dfrac{y}{24}=\dfrac{-12}{18}\)
\(\Rightarrow\dfrac{4}{x-6}=\dfrac{-12}{18}\)
\(\Rightarrow x-6=\dfrac{18.4}{-12}=-6\)
\(\Rightarrow x=0\)
\(\Rightarrow\dfrac{y}{24}=\dfrac{-12}{18}\)
\(\Rightarrow y=\dfrac{-12.24}{18}=-16\)
\(\dfrac{3-x}{-12}=\dfrac{16}{y+1}=\dfrac{192}{-72}\)
\(\Rightarrow\dfrac{3-x}{-12}=\dfrac{192}{-72}\)
\(\Rightarrow3-x=\dfrac{192.-12}{-72}=32\)
\(\Rightarrow x=-29\)
\(\Rightarrow\dfrac{16}{y+1}=\dfrac{192}{-72}\)
\(\Rightarrow y+1=\dfrac{16.-72}{192}=-6\)
d) \(\dfrac{-2}{3}< \dfrac{x}{5}< \dfrac{-1}{6}\)
\(\Rightarrow\dfrac{-20}{30}< \dfrac{6x}{30}< \dfrac{-5}{30}\)
\(\Rightarrow6x\in\left\{-18;-12;-6\right\}\)
\(\Rightarrow x\in\left\{-3;-2;-1\right\}\)
\(\dfrac{-1}{5}\le\dfrac{x}{8}\le\dfrac{1}{4}\)
\(\Rightarrow\dfrac{-8}{40}\le\dfrac{5x}{40}\le\dfrac{10}{40}\)
\(\Rightarrow5x\in\left\{-5;0;5;10\right\}\)
\(\Rightarrow x\in\left\{-1;0;1;2\right\}\)
e) \(\dfrac{x+46}{20}=x\dfrac{2}{5}\)
\(\Rightarrow\dfrac{x+46}{20}=x+\dfrac{2}{5}\)
\(\Rightarrow\dfrac{x+46}{20}=\dfrac{5x+2}{5}\)
\(\Rightarrow5.\left(x+46\right)=20.\left(5x+2\right)\)
\(\Rightarrow5x+230=100x+40\)
\(\Rightarrow5x-100x=40-230\)
\(\Rightarrow-95x=-190\)
\(\Rightarrow x=-190:-95\)
\(\Rightarrow x=2\)
\(y\dfrac{5}{y}=\dfrac{86}{y}\)
\(\Rightarrow y+\dfrac{5}{y}=\dfrac{86}{y}\)
\(\Rightarrow\dfrac{y^2+5}{y}=\dfrac{86}{y}\)
\(\Rightarrow y^2+5=86\)
\(\Rightarrow y^2=86-5\)
\(\Rightarrow y^2=81\)
\(\Rightarrow\left[{}\begin{matrix}y=9\\y=-9\end{matrix}\right.\)
Chúc bạn học tốt!
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a) Quy đồng mẫu số ta được: 30/6x-yx2/6x=x/6x
suy ra 30-yx = x <=> x.y=30-x
Xong bạn liệt kê ra vì có khác nhiều đáp số đó.
Phần b) và c) tương tự vậy !!!
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\(a,\frac{5}{x}-\frac{y}{3}=\frac{1}{6}\)
\(\Leftrightarrow x=2;1\)vì quy đồng mẫu số : 2.3=6 ; 3.2=6
hoặc : 1.6=6 ; 3.2=6
Nếu x = 1 thì ta có :
\(\frac{5}{1}-\frac{y}{3}=\frac{1}{6}\Leftrightarrow\frac{30}{6}-\frac{y.2}{6}\Leftrightarrow y.2=30-1\Leftrightarrow y=\frac{30-1}{2}\)
=> y ko có kết quả vì 29 ko chia hết cho 2
Nếu x = 2 thì ta có :
\(\frac{5}{2}-\frac{y}{3}=\frac{1}{6}\Leftrightarrow\frac{15}{6}-\frac{y.2}{6}\Leftrightarrow y.2=15-1\Leftrightarrow y=\frac{15-1}{2}\Leftrightarrow y=14:2\Leftrightarrow y=7\)
Vay ..........
Câu b tương tự
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1) \(\frac{3}{x}+\frac{y}{3}=\frac{5}{6}\)
\(\Leftrightarrow\frac{3}{x}=\frac{5}{6}-\frac{y}{3}\)
\(\Leftrightarrow\frac{3}{x}=\frac{5}{6}-\frac{2y}{6}\)
\(\Leftrightarrow\frac{3}{x}=\frac{5-2y}{6}\)
\(\Leftrightarrow x.\left(5-2y\right)=3.6\)
\(\Leftrightarrow x.\left(5-2y\right)=18\)
Mà \(x,y\in Z\Rightarrow5-2y\in Z\)
Lập bảng tìm nốt
\(\frac{x}{6}-\frac{2}{y}=\frac{1}{30}\)
\(\Leftrightarrow\frac{2}{y}=\frac{x}{6}-\frac{1}{30}\)
\(\Leftrightarrow\frac{2}{y}=\frac{5x}{30}-\frac{1}{30}\)
\(\Leftrightarrow\frac{2}{y}=\frac{5x-1}{30}\)
\(\Leftrightarrow y(5x-1)=60\)
Làm nốt , đến đây dễ rồi
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\(2,\frac{9}{x}=\frac{2}{5}-\frac{7}{20}\)
\(\Rightarrow\frac{9}{x}=\frac{1}{20}\)
\(\Rightarrow x=9.20\)
\(\Rightarrow x=180\)
\(\frac{x}{5}=\frac{5}{6}+\left(-\frac{19}{30}\right)\)
\(\frac{\Rightarrow x}{5}=\frac{1}{5}\)
\(\Rightarrow x=1\)
Giải:
a) \(\frac{3}{x}+\frac{y}{5}=\frac{5}{6}\)
=> \(\frac{3}{x}=\frac{5}{6}-\frac{y}{5}\)
=> \(\frac{3}{x}=\frac{25}{30}-\frac{6y}{30}\)
=> \(\frac{3}{x}=\frac{25-6y}{30}\)
=> \(x\left(25-6y\right)=90\)=> \(x\left(25-6y\right)\inƯ\left(90\right)=\left\{1;2;3;5;6;9;10;15;30;90\right\}\)
Lập bảng (vì đề không cho cái gì , không cho điều kiện)
Vậy : x = 90,y = 4
b) \(\frac{x}{6}-\frac{2}{y}=\frac{1}{30}\)
=> \(\frac{2}{y}=\frac{x}{6}-\frac{1}{30}=\frac{5x}{30}-\frac{1}{30}=\frac{5x-1}{30}\)
=> y(5x - 1) = 60
Cũng tương tự như câu a