Solve 3/8x-5/9+4/5y+2/3+frac{3}{4}x+frac{6}{5}y

$$\frac { 3 } { 8 } x - \frac { 5 } { 9 } + \frac { 4 } { 5 } y + \frac { 2 } { 3 } + \frac { 3 } { 4 } x + \frac { 6 } { 5 } y$$

Evaluate

$$\frac{9x}{8}+2y+\frac{1}{9}$$

Solution Steps

Least common multiple of 9 and 3 is 9. Convert -\frac{5}{9} and \frac{2}{3} to fractions with denominator 9.

$$\frac{3}{8}x-\frac{5}{9}+\frac{4}{5}y+\frac{6}{9}+\frac{3}{4}x+\frac{6}{5}y$$

Since -\frac{5}{9} and \frac{6}{9} have the same denominator, add them by adding their numerators.

$$\frac{3}{8}x+\frac{-5+6}{9}+\frac{4}{5}y+\frac{3}{4}x+\frac{6}{5}y$$

Add -5 and 6 to get 1.

$$\frac{3}{8}x+\frac{1}{9}+\frac{4}{5}y+\frac{3}{4}x+\frac{6}{5}y$$

Combine \frac{3}{8}x and \frac{3}{4}x to get \frac{9}{8}x.

$$\frac{9}{8}x+\frac{1}{9}+\frac{4}{5}y+\frac{6}{5}y$$

Combine \frac{4}{5}y and \frac{6}{5}y to get 2y.

$$\frac{9}{8}x+\frac{1}{9}+2y$$

Factor

$$\frac{81x+144y+8}{72}$$

Solution Steps

Factor out \frac{1}{360}.

$$\frac{405x+40+720y}{360}$$

Consider 135x-200+288y+240+270x+432y. Multiply and combine like terms.

$$405x+720y+40$$

Consider 405x+720y+40. Factor out 5.

$$5\left(81x+144y+8\right)$$

Rewrite the complete factored expression.

$$\frac{81x+144y+8}{72}$$