Question

Le t $D_{1}=\begin{vmatrix}a&b&a+b\\ c&b&c+d\\ a&b&a-b\end{vmatrix}$ and $D_{2}=\begin{vmatrix}a&c&a+c\\ b&d&b+d\\ a&c&a+b+c\end{vmatrix}$ then the value of $D_{1} / D_{2}$ is, where $b \neq 0$ and $a d \neq b c$ ___.

Answer 1

Using: $C_{3} \rightarrow C_{3}-\left(C_{1}+C_{2}\right)$ in $D_{1}$ and $D_{2},$ we have
$\therefore \frac{D_{1}}{D_{2}}=\frac{-2 b(a d-b c)}{b(a d-b c)}=-2$