Solve 1/5x+4/5y+2/5x-1/5y-frac{2}{3}z+frac{1}{3}z=

$$\frac { 1 } { 5 } x + \frac { 4 } { 5 } y + \frac { 2 } { 5 } x - \frac { 1 } { 5 } y - \frac { 2 } { 3 } z + \frac { 1 } { 3 } z =$$

Evaluate

$$\frac{3x}{5}+\frac{3y}{5}-\frac{z}{3}$$

Solution Steps

Combine \frac{1}{5}x and \frac{2}{5}x to get \frac{3}{5}x.

$$\frac{3}{5}x+\frac{4}{5}y-\frac{1}{5}y-\frac{2}{3}z+\frac{1}{3}z$$

Combine \frac{4}{5}y and -\frac{1}{5}y to get \frac{3}{5}y.

$$\frac{3}{5}x+\frac{3}{5}y-\frac{2}{3}z+\frac{1}{3}z$$

Combine -\frac{2}{3}z and \frac{1}{3}z to get -\frac{1}{3}z.

$$\frac{3}{5}x+\frac{3}{5}y-\frac{1}{3}z$$

Factor

$$\frac{9x+9y-5z}{15}$$

Solution Steps

Factor out \frac{1}{15}.

$$\frac{3x+12y+6x-3y-10z+5z}{15}$$

Consider 3x+12y+6x-3y-10z+5z. Multiply and combine like terms.

$$9x+9y-5z$$

Rewrite the complete factored expression.

$$\frac{9x+9y-5z}{15}$$