Ta có: \(\frac{x}{3}-\frac{5}{y}=\frac{1}{6}\)

\(\Leftrightarrow\frac{xy-15}{3y}=\frac{1}{6}\)

\(\Leftrightarrow6xy-90=3y\)

\(\Leftrightarrow2xy-y=30\)

\(\Leftrightarrow y\left(2x-1\right)=30\)

Đến đây xét ước là ok rồi

=>\(\dfrac{3}{x-5}-\dfrac{y}{3}=\dfrac{1}{6}\)

=>\(\dfrac{9-y\left(x-5\right)}{3\left(x-5\right)}=\dfrac{1}{6}\)

=>9-y(x-5)=1/2(x-5)

=>(x-5)(1/2+y)=9

=>(x-5)(2y+1)=18

=>\(\left(x-5;2y+1\right)\in\left\{\left(18;1\right);\left(-18;-1\right);\left(2;9\right);\left(-2;-9\right);\left(6;3\right);\left(-6;-3\right)\right\}\)

=>\(\left(x,y\right)\in\left\{\left(23;0\right);\left(-13;-1\right);\left(7;4\right);\left(3;-5\right);\left(11;1\right);\left(-1;-2\right)\right\}\)

\(x-\frac{3}{5}=1\div3\)

\(x-\frac{3}{5}=\frac{1}{3}\)

\(x=\frac{1}{3}+\frac{3}{5}=\frac{14}{15}\)

Chắc x 1/6 = 5 : 4 là phép nhân

\(x\times\frac{1}{6}=5\div4\)

\(x\times\frac{1}{6}=\frac{5}{4}\)

\(x=\frac{5}{4}\div\frac{1}{6}\)

\(x=\frac{15}{2}\)

x-3/5=1/3

x=1/3+3/5

x=14/15

x.1/6=5/4

x=5/4:1/6

x=5/4x6

x=15/2

\(\dfrac{2}{30}\)

`(1 xx 2 xx 3 xx 4)/(3 xx 4 xx 5 xx 6)`

`= (1 xx 2)/(5 xx 6)`

`= 2/12`

`= 1/6`

Giải cách phương trình sau

2.(x+3/5)=5-(13/5+x)

=> 2x + 6/5 = 5 - 13/5 - x

=> 2x + x = 12/5 - 6/5

=> 3x = 6/5

=> x = 2/5

=> 1/x = 5/6 - y/3

1/x = 5-2y/6

=> x(5-2y) = 1.6 = 6

Do x ∈ N => x >= 0

Mà 6>0 => 5-2y > 0

Vì y ∈ N => 5-2y ∈ N*

Ta có bảng:

Do x,y ∈ N => (x,y) = (6,2) (thử lại thỏa mãn)

Vậy x=6; y = 2

ai hỏi

\(\left(6:3,5-1\dfrac{1}{6}\times\dfrac{6}{7}\right):\left(4,2\times\dfrac{10}{11}+5\dfrac{2}{11}\right)\\ =\left(\dfrac{12}{7}-\dfrac{7}{6}\times\dfrac{6}{7}\right):\left(\dfrac{21}{5}\times\dfrac{10}{11}+\dfrac{57}{11}\right)\\ =\left(\dfrac{17}{7}-1\right):\left(\dfrac{42}{11}+\dfrac{57}{11}\right)\\ =\dfrac{10}{7}:9\\ =\dfrac{10}{63}\)

\(\left(6:\dfrac{3}{5}-1\dfrac{1}{6}\times\dfrac{6}{7}\right):\left(4,2\times\dfrac{10}{11}+5\dfrac{2}{11}\right)\)

\(=\left(6\times\dfrac{5}{3}-\dfrac{7}{6}\times\dfrac{6}{7}\right):\left(\dfrac{21}{5}\times\dfrac{10}{11}+\dfrac{57}{11}\right)\)

\(=\left(10-1\right):\left(\dfrac{42}{11}+\dfrac{57}{11}\right)=9:9=1\)

16:Sửa đề: \(\frac12x+\frac16\left(x-2\right)=\frac34-2x\)

=>\(\frac12x+\frac16x-\frac26=\frac34-2x\)

=>\(\frac46x-\frac13=\frac34-2x\)

=>\(\frac23x+2x=\frac34+\frac13\)

=>\(\frac83x=\frac{9}{12}+\frac{4}{12}=\frac{13}{12}\)

=>\(x=\frac{13}{12}:\frac83=\frac{13}{12}\times\frac38=\frac{13}{4\times8}=\frac{13}{32}\)

19: \(\frac{5}{12}x+3=\frac13-\frac{7}{12}x\)

=>\(\frac{5}{12}x+\frac{7}{12}x=\frac13-3\)

=>\(\frac{12}{12}x=\frac13-\frac93=-\frac83\)

=>\(x=-\frac83\)

20: \(\frac12x+\frac52=\frac72x-\frac34\)

=>\(\frac12x-\frac72x=-\frac34-\frac52\)

=>\(-3x=-\frac34-\frac{10}{4}=-\frac{13}{4}\)

=>\(3x=\frac{13}{4}\)

=>\(x=\frac{13}{4}:3=\frac{13}{12}\)