tìm tất cả các cặp số nguyên x,y thỏa mãn:x(2y+3)=y+1

$x(2y+3)=y+1$

$⇒2xy+3x=y+1$

$⇒2xy+3x-(y+1)=0$

$⇒2xy+3x-y-1=0$

$⇒2xy+3x-y=1$

$⇒x(2y+3)-y=1$

$⇒2x(2y+3)-2y=1.2$

$⇒2x(2y+3)-2y-3=2-3$

$⇒2x(2y+3)-(2y+3)=-1$

$⇒(2x-1)(2y+3)=-1$

$⇒2x-1;2y+3∈Ư(-1)=±1$

$\left[\begin{array}{ccc}2x-1&1&-1\\2y+3&-1&1\\x&1&0\\y&-2&-1\end{array}\right]$

$Vậy$ $(x;y)=(1;-2);(0;-1)$