Factor out the common term \(2\).
\[\frac{5}{2(p-2)}-\frac{2}{6-3p}\]
Factor out the common term \(3\).
\[\frac{5}{2(p-2)}-\frac{2}{3(2-p)}\]
Rewrite the expression with a common denominator.
\[\frac{5\times 3(2-p)-2\times 2(p-2)}{2(p-2)\times 3(2-p)}\]
Simplify \(5\times 3(2-p)\) to \(15(2-p)\).
\[\frac{15(2-p)-2\times 2(p-2)}{2(p-2)\times 3(2-p)}\]
Simplify \(2\times 2(p-2)\) to \(4(p-2)\).
\[\frac{15(2-p)-4(p-2)}{2(p-2)\times 3(2-p)}\]
Expand.
\[\frac{30-15p-4p+8}{2(p-2)\times 3(2-p)}\]
Collect like terms.
\[\frac{(30+8)+(-15p-4p)}{2(p-2)\times 3(2-p)}\]
Simplify \((30+8)+(-15p-4p)\) to \(38-19p\).
\[\frac{38-19p}{2(p-2)\times 3(2-p)}\]
Factor out the common term \(19\).
\[\frac{19(2-p)}{2(p-2)\times 3(2-p)}\]
Simplify \(2(p-2)\times 3(2-p)\) to \(6(p-2)(2-p)\).
\[\frac{19(2-p)}{6(p-2)(2-p)}\]
Cancel \(2-p\).
\[\frac{19}{6(p-2)}\]
19/(6*(p-2))
