$\begin{array} { l }\frac{ 10 }{ x+8 }=\frac{ 160 }{ 108 },& x≠-8\end{array}$
Cancel out the common factor $4$$\frac{ 10 }{ x+8 }=\frac{ 40 }{ 27 }$
Simplify the equation using cross-multiplication$270=40\left( x+8 \right)$
Distribute $40$ through the parentheses$270=40x+320$
Move the variable to the left-hand side and change its sign$270-40x=320$
Move the constant to the right-hand side and change its sign$-40x=320-270$
Subtract the numbers$-40x=50$
Divide both sides of the equation by $-40$$\begin{array} { l }x=-\frac{ 5 }{ 4 },& x≠-8\end{array}$
Check if the solution is in the defined range$\begin{align*}&x=-\frac{ 5 }{ 4 } \\&\begin{array} { l }x=-1 \frac{ 1 }{ 4 },& x=-1.25\end{array}\end{align*}$