Solve 2/3x-3/5y+5/3xy-2/5x+frac{4}{3}y-frac{3}{4}xy-frac{1}{5}x+frac{3}{15}y+frac{2}{6}xy

$$\frac { 2 } { 3 } x - \frac { 3 } { 5 } y + \frac { 5 } { 3 } x y - \frac { 2 } { 5 } x + \frac { 4 } { 3 } y - \frac { 3 } { 4 } x y - \frac { 1 } { 5 } x + \frac { 3 } { 15 } y + \frac { 2 } { 6 } x y$$

Evaluate

$$\frac{5xy}{4}+\frac{x}{15}+\frac{14y}{15}$$

Solution Steps

Combine \frac{2}{3}x and -\frac{2}{5}x to get \frac{4}{15}x.

$$\frac{4}{15}x-\frac{3}{5}y+\frac{5}{3}xy+\frac{4}{3}y-\frac{3}{4}xy-\frac{1}{5}x+\frac{3}{15}y+\frac{2}{6}xy$$

Combine -\frac{3}{5}y and \frac{4}{3}y to get \frac{11}{15}y.

$$\frac{4}{15}x+\frac{11}{15}y+\frac{5}{3}xy-\frac{3}{4}xy-\frac{1}{5}x+\frac{3}{15}y+\frac{2}{6}xy$$

Combine \frac{5}{3}xy and -\frac{3}{4}xy to get \frac{11}{12}xy.

$$\frac{4}{15}x+\frac{11}{15}y+\frac{11}{12}xy-\frac{1}{5}x+\frac{3}{15}y+\frac{2}{6}xy$$

Combine \frac{4}{15}x and -\frac{1}{5}x to get \frac{1}{15}x.

$$\frac{1}{15}x+\frac{11}{15}y+\frac{11}{12}xy+\frac{3}{15}y+\frac{2}{6}xy$$

Reduce the fraction \frac{3}{15} to lowest terms by extracting and canceling out 3.

$$\frac{1}{15}x+\frac{11}{15}y+\frac{11}{12}xy+\frac{1}{5}y+\frac{2}{6}xy$$

Combine \frac{11}{15}y and \frac{1}{5}y to get \frac{14}{15}y.

$$\frac{1}{15}x+\frac{14}{15}y+\frac{11}{12}xy+\frac{2}{6}xy$$

Reduce the fraction \frac{2}{6} to lowest terms by extracting and canceling out 2.

$$\frac{1}{15}x+\frac{14}{15}y+\frac{11}{12}xy+\frac{1}{3}xy$$

Combine \frac{11}{12}xy and \frac{1}{3}xy to get \frac{5}{4}xy.

$$\frac{1}{15}x+\frac{14}{15}y+\frac{5}{4}xy$$

Factor

$$\frac{75xy+4x+56y}{60}$$

Solution Steps

Factor out \frac{1}{60}.

$$\frac{40x-36y+100xy-24x+80y-45xy-12x+12y+20xy}{60}$$