\(\dfrac{12x}{x-9}-\dfrac{x-10}{81-x^2}\)
\(=\dfrac{12x}{x-9}+\dfrac{x-10}{x^2-81}\)
\(=\dfrac{12x\left(x+9\right)}{\left(x-9\right)\left(x+9\right)}+\dfrac{x-10}{\left(x-9\right)\left(x+9\right)}\)
\(=\dfrac{12x^2+108x+x-10}{\left(x-9\right)\left(x+9\right)}\)
\(=\dfrac{12x^2+109x-10}{\left(x-9\right)\left(x+9\right)}\)