Solve -1/3{e}^-frac{1{3}x}left(-2/3+1/9xright)+{e}^-frac{1{3}x}1/9

$$- \frac{ 1 }{ 3 } { e }^{ - \frac{ 1 }{ 3 } x } \left( - \frac{ 2 }{ 3 } + \frac{ 1 }{ 9 } x \right) + { e }^{ - \frac{ 1 }{ 3 } x } \frac{ 1 }{ 9 }$$

Factor

$$\frac{\left(9-x\right)e^{-\frac{x}{3}}}{27}$$

Solution Steps

Factor out \frac{1}{27}.

$$\frac{-e^{-\frac{x}{3}}\left(-6+x\right)+3e^{-\frac{x}{3}}}{27}$$

Consider -e^{-\frac{1}{3}x}\left(-6+x\right)+3e^{-\frac{1}{3}x}. Factor out e^{-\frac{x}{3}}.

$$e^{-\frac{x}{3}}\left(-\left(-6+x\right)+3\right)$$

Consider -\left(-6+x\right)+3. Multiply and combine like terms.

$$-x+9$$

Rewrite the complete factored expression.

$$\frac{e^{-\frac{x}{3}}\left(-x+9\right)}{27}$$

Evaluate

$$\frac{\left(9-x\right)e^{-\frac{x}{3}}}{27}$$