Calculate: (3)/(2)=(a-3)/(a+1)

Expression: $\frac{ 3 }{ 2 }=\frac{ a-3 }{ a+1 }$

Determine the defined range

$\begin{array} { l }\frac{ 3 }{ 2 }=\frac{ a-3 }{ a+1 },& a≠-1\end{array}$

Simplify the equation using cross-multiplication

$3\left( a+1 \right)=2\left( a-3 \right)$

Distribute $3$ through the parentheses

$3a+3=2\left( a-3 \right)$

Distribute $2$ through the parentheses

$3a+3=2a-6$

Move the variable to the left-hand side and change its sign

$3a+3-2a=-6$

Move the constant to the right-hand side and change its sign

$3a-2a=-6-3$

Collect like terms

$a=-6-3$

Calculate the difference

$\begin{array} { l }a=-9,& a≠-1\end{array}$

Check if the solution is in the defined range

$a=-9$