Simplify \(a\times \frac{2}{3}\) to \(\frac{a\times 2}{3}\).
\[\frac{\frac{a\times 2}{3}+b\times \frac{2}{3}}{a-b}-\frac{1}{a\times \frac{1}{3}-b\times \frac{1}{3}}\]
Regroup terms.
\[\frac{\frac{2a}{3}+b\times \frac{2}{3}}{a-b}-\frac{1}{a\times \frac{1}{3}-b\times \frac{1}{3}}\]
Simplify \(b\times \frac{2}{3}\) to \(\frac{b\times 2}{3}\).
\[\frac{\frac{2a}{3}+\frac{b\times 2}{3}}{a-b}-\frac{1}{a\times \frac{1}{3}-b\times \frac{1}{3}}\]
Regroup terms.
\[\frac{\frac{2a}{3}+\frac{2b}{3}}{a-b}-\frac{1}{a\times \frac{1}{3}-b\times \frac{1}{3}}\]
Factor out the common term \(2\).
\[\frac{2(\frac{a}{3}+\frac{b}{3})}{a-b}-\frac{1}{a\times \frac{1}{3}-b\times \frac{1}{3}}\]
Join the denominators.
\[\frac{2\times \frac{a+b}{3}}{a-b}-\frac{1}{a\times \frac{1}{3}-b\times \frac{1}{3}}\]
Simplify \(2\times \frac{a+b}{3}\) to \(\frac{2(a+b)}{3}\).
\[\frac{\frac{2(a+b)}{3}}{a-b}-\frac{1}{a\times \frac{1}{3}-b\times \frac{1}{3}}\]
Simplify \(a\times \frac{1}{3}\) to \(\frac{a}{3}\).
\[\frac{\frac{2(a+b)}{3}}{a-b}-\frac{1}{\frac{a}{3}-b\times \frac{1}{3}}\]
Simplify \(b\times \frac{1}{3}\) to \(\frac{b}{3}\).
\[\frac{\frac{2(a+b)}{3}}{a-b}-\frac{1}{\frac{a}{3}-\frac{b}{3}}\]
Join the denominators.
\[\frac{\frac{2(a+b)}{3}}{a-b}-\frac{1}{\frac{a-b}{3}}\]
Simplify \(\frac{\frac{2(a+b)}{3}}{a-b}\) to \(\frac{2(a+b)}{3(a-b)}\).
\[\frac{2(a+b)}{3(a-b)}-\frac{1}{\frac{a-b}{3}}\]
Invert and multiply.
\[\frac{2(a+b)}{3(a-b)}-\frac{3}{a-b}\]
Rewrite the expression with a common denominator.
\[\frac{2(a+b)-3\times 3}{3(a-b)}\]
Simplify \(3\times 3\) to \(9\).
\[\frac{2(a+b)-9}{3(a-b)}\]
(2*(a+b)-9)/(3*(a-b))
