<=>xy+x+y-1=0

<=>x(y+1)-(y+1)=0

<=>(y+1)(x-1)=0

<=> y+1=0 <=>y=-1

hoặc x-1=0<=>x=1

\(\frac{x+4}{2000}+\frac{x+3}{2001}=\frac{x+2}{2002}+\frac{x+1}{2003}\)

\(\Rightarrow\left(\frac{x+4}{2000}+1\right)+\left(\frac{x+3}{2001}+1\right)=\left(\frac{x+2}{2002}+1\right)+\left(\frac{x+1}{2003}+1\right)\)

\(\Rightarrow\frac{x+2004}{2000}+\frac{x+4}{2001}=\frac{x+4}{2002}+\frac{x+4}{2003}\)

\(\Rightarrow\frac{x+2004}{2000}+\frac{x+2004}{2001}-\frac{x+2004}{2002}-\frac{x+2004}{2003}=0\)

\(\Rightarrow\left(x+2004\right)\left(\frac{1}{2000}+\frac{1}{2001}-\frac{1}{2002}-\frac{1}{2003}\right)=0\)

vì \(\frac{1}{2000}+\frac{1}{2001}-\frac{1}{2002}-\frac{1}{2003}\ne0\Rightarrow x+2004=0\)

=>x=-2004

vậy x=-2004

\(\frac{x+1}{10}+\frac{x+1}{11}+\frac{x+1}{12}=\frac{x+1}{13}+\frac{x+1}{14}\)

\(\Rightarrow\frac{x+1}{10}+\frac{x+1}{11}+\frac{x+1}{12}-\frac{x+1}{13}-\frac{x+1}{14}=0\)

\(\Rightarrow\left(x+1\right)\left(\frac{1}{10}+\frac{1}{11}+\frac{1}{12}-\frac{1}{13}-\frac{1}{14}\right)=0\)

\(\frac{1}{10}+\frac{1}{11}+\frac{1}{12}-\frac{1}{13}-\frac{1}{14}\ne0\Rightarrow x+1=0\)

=>x=-1

vậy x=-1

\(\frac{x}{3}=\frac{y}{4}=\frac{z}{5}\Rightarrow\frac{x^2}{9}=\frac{y^2}{16}=\frac{z^2}{25}\)

Áp dụng tính chất dãy tỉ số bằng nhau ta có

\(\frac{x^2}{9}=\frac{y^2}{16}=\frac{z^2}{25}=\frac{2x^2+2y^2-3z^2}{2\cdot9+2\cdot16-3\cdot25}=\frac{-100}{-25}=4\)

\(\Rightarrow x^2=36;y^2=64;z^2=100\)

\(\Rightarrow\) x = + 6; y = + 8; z = + 10

\(\frac{7}{3}:\left(4.x-1\right)^2-\frac{1}{4}=\frac{1}{3}\)

\(\frac{7}{3}:\left(4.x-1\right)^2=\frac{1}{3}+\frac{1}{4}\)

\(\frac{7}{3}:\left(4.x-1\right)^2=\frac{7}{12}\)

\(\left(4.x-1\right)^2=\frac{7}{3}:\frac{7}{12}\)

\(\left(4.x-1\right)^2=4\)

\(\left(4.x-1\right)^2=2^2\)

\(4.x-1=2\)

\(4.x=2+1\)

\(4.x=3\)

\(x=3:4\)

\(x=0,75\)

 X x 10 + ( ( 28+1 ) x 10 : 2 = 156

 X x 10 + ( 29 x 10 : 2 )      = 156

X x 10 + 145                     = 156 - 145

X x 10                               =11

X                                     = 11 : 10

X                                     =  1,1

tick mình nha !