The difference is [tex]$\frac{3 x+81}{x(x-9)(x+9)}$[/tex]
Explanation:
The expression is [tex]$\left(\frac{9}{x^{2}-9 x}\right)-\left(\frac{6}{x^{2}-81}\right)$[/tex]
Removing the parenthesis, we have,
[tex]$\left\frac{9}{x^{2}-9 x}\right-\left\frac{6}{x^{2}-81}\right$[/tex]
Factoring the terms [tex]$x^{2}-9 x$[/tex] and [tex]$x^{2}-81$[/tex], we get,
[tex]$\frac{9}{x(x-9)}-\frac{6}{(x+9)(x-9)}$[/tex]
Taking LCM, we get,
[tex]$\frac{9(x+9)-6x}{x(x-9)(x+9)}}$[/tex]
Simplifying the numerator, we get,
[tex]$\frac{9x+81-6x}{x(x-9)(x+9)}}$[/tex]
Subtracting the numerator, we have,
[tex]$\frac{3 x+81}{x(x-9)(x+9)}$[/tex]
Hence, the difference is [tex]$\frac{3 x+81}{x(x-9)(x+9)}$[/tex]
