$\begin{array} { l }\frac{ x }{ x-9 }-\frac{ 8 }{ x+2 }=\frac{ 0x+99 }{ {x}^{2}-7x-18 },& \begin{array} { l }x≠9,& x≠-2\end{array}\end{array}$
Any expression multiplied by $0$ equals $0$$\frac{ x }{ x-9 }-\frac{ 8 }{ x+2 }=\frac{ 0+99 }{ {x}^{2}-7x-18 }$
Removing $0$ doesn't change the value, so remove it from the expression$\frac{ x }{ x-9 }-\frac{ 8 }{ x+2 }=\frac{ 99 }{ {x}^{2}-7x-18 }$
Move the expression to the left-hand side and change its sign$\frac{ x }{ x-9 }-\frac{ 8 }{ x+2 }-\frac{ 99 }{ {x}^{2}-7x-18 }=0$
Write $-7x$ as a difference$\frac{ x }{ x-9 }-\frac{ 8 }{ x+2 }-\frac{ 99 }{ {x}^{2}+2x-9x-18 }=0$
Factor out $x$ from the expression$\frac{ x }{ x-9 }-\frac{ 8 }{ x+2 }-\frac{ 99 }{ x \times \left( x+2 \right)-9x-18 }=0$
Factor out $-9$ from the expression$\frac{ x }{ x-9 }-\frac{ 8 }{ x+2 }-\frac{ 99 }{ x \times \left( x+2 \right)-9\left( x+2 \right) }=0$
Factor out $x+2$ from the expression$\frac{ x }{ x-9 }-\frac{ 8 }{ x+2 }-\frac{ 99 }{ \left( x+2 \right) \times \left( x-9 \right) }=0$
Write all numerators above the least common denominator $\left( x+2 \right) \times \left( x-9 \right)$$\frac{ x \times \left( x+2 \right)-8\left( x-9 \right)-99 }{ \left( x+2 \right) \times \left( x-9 \right) }=0$
Distribute $x$ through the parentheses$\frac{ {x}^{2}+2x-8\left( x-9 \right)-99 }{ \left( x+2 \right) \times \left( x-9 \right) }=0$
Distribute $-8$ through the parentheses$\frac{ {x}^{2}+2x-8x+72-99 }{ \left( x+2 \right) \times \left( x-9 \right) }=0$
Collect like terms$\frac{ {x}^{2}-6x+72-99 }{ \left( x+2 \right) \times \left( x-9 \right) }=0$
Calculate the difference$\frac{ {x}^{2}-6x-27 }{ \left( x+2 \right) \times \left( x-9 \right) }=0$
Write $-6x$ as a difference$\frac{ {x}^{2}+3x-9x-27 }{ \left( x+2 \right) \times \left( x-9 \right) }=0$
Factor out $x$ from the expression$\frac{ x \times \left( x+3 \right)-9x-27 }{ \left( x+2 \right) \times \left( x-9 \right) }=0$
Factor out $-9$ from the expression$\frac{ x \times \left( x+3 \right)-9\left( x+3 \right) }{ \left( x+2 \right) \times \left( x-9 \right) }=0$
Factor out $x+3$ from the expression$\frac{ \left( x+3 \right) \times \left( x-9 \right) }{ \left( x+2 \right) \times \left( x-9 \right) }=0$
Cancel out the common factor $x-9$$\frac{ x+3 }{ x+2 }=0$
When the quotient of expressions equals $0$, the numerator has to be $0$$x+3=0$
Move the constant to the right-hand side and change its sign$\begin{array} { l }x=-3,& \begin{array} { l }x≠9,& x≠-2\end{array}\end{array}$
Check if the solution is in the defined range$x=-3$