a:
ĐKXĐ: y<>0
x/19=1/y
=>xy=19
=>\(x\cdot y=1\cdot19=19\cdot1=\left(-1\right)\cdot\left(-19\right)=\left(-19\right)\cdot\left(-1\right)\)
=>\(\left(x,y\right)\in\left\{\left(1;19\right);\left(19;1\right);\left(-1;-19\right);\left(-19;-1\right)\right\}\)
b: ĐKXĐ: y<>3
\(\dfrac{x+2}{23}=\dfrac{1}{y-3}\)
=>\(\left(x+2\right)\left(y-3\right)=23\)
=>\(\left(x+2\right)\left(y-3\right)=1\cdot23=23\cdot1=\left(-1\right)\cdot\left(-23\right)=\left(-23\right)\cdot\left(-1\right)\)
=>\(\left(x+2;y-3\right)\in\left\{\left(1;23\right);\left(23;1\right);\left(-1;-23\right);\left(-23;-1\right)\right\}\)
=>\(\left(x,y\right)\in\left\{\left(-1;26\right);\left(21;4\right);\left(-3;-20\right);\left(-25;2\right)\right\}\)
\(a,x.y=19\Rightarrow x,y\inƯ\left(19\right)=\left\{-19;-1;1;19\right\}\\ Với:x=-19\Rightarrow y=-1\\ Với:x=-1\Rightarrow y=-19\\ Với:x=1\Rightarrow y=19\\ Với:x=19\Rightarrow y=1\\ Vậy:\left(x;y\right)\in\left\{\left(-19;-1\right);\left(-1;-19\right);\left(1;19\right);\left(19;1\right)\right\}\\ ---\\ b,\dfrac{x+2}{23}=\dfrac{-1}{y-3}\\ \Rightarrow\left(x+2\right)\left(y-3\right)=-1.23=-23\\ Vậy:\left(x+2\right),\left(y-3\right)\inƯ\left(-23\right)=\left\{-23;-1;1;23\right\}\\ Với:x+2=-23;y-3=1\Rightarrow x=-25;y=4\\ Với:x+2=-1;y-3=23\Rightarrow x=-3;y=26\\ Với:x+2=1;y-3=-23\Rightarrow x=-1;y=-20\\ Với:x+2=23;y-3=-1\Rightarrow x=21;y=2\\ Vậy:\left(x;y\right)\in\left\{\left(-25;4\right);\left(-3;26\right);\left(-1;-20\right);\left(21;2\right)\right\}\)