Evaluate: (-6)/(x^2-16)-(9)/(16-x^2)

Expression: $\frac{ -6 }{ {x}^{2}-16 }-\frac{ 9 }{ 16-{x}^{2} }$

Use $\frac{ -a }{ b }=\frac{ a }{ -b }=-\frac{ a }{ b }$ to rewrite the fraction

$-\frac{ 6 }{ {x}^{2}-16 }-\frac{ 9 }{ 16-{x}^{2} }$

Factor out the negative sign from the expression and reorder the terms

$-\frac{ 6 }{ {x}^{2}-16 }-\frac{ 9 }{ -\left( {x}^{2}-16 \right) }$

Determine the sign of the fraction

$-\frac{ 6 }{ {x}^{2}-16 }+\frac{ 9 }{ {x}^{2}-16 }$

Write all numerators above the common denominator

$\frac{ 3 }{ {x}^{2}-16 }$