Solve 3x/8+(5y/6-3x/4+2y/3)

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

Evaluate

$$\frac{3y}{2}-\frac{3x}{8}$$

Short Solution Steps

Combine \frac{3x}{8} and -\frac{3x}{4} to get -\frac{1}{8}\times 3x.

$$-\frac{1}{8}\times 3x+\frac{5y}{6}+\frac{2y}{3}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 6 and 3 is 6. Multiply \frac{2y}{3} times \frac{2}{2}.

$$-\frac{1}{8}\times 3x+\frac{5y}{6}+\frac{2\times 2y}{6}$$

Since \frac{5y}{6} and \frac{2\times 2y}{6} have the same denominator, add them by adding their numerators.

$$-\frac{1}{8}\times 3x+\frac{5y+2\times 2y}{6}$$

Do the multiplications in 5y+2\times 2y.

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

Combine like terms in 5y+4y.

$$-\frac{1}{8}\times 3x+\frac{9y}{6}$$

Express -\frac{1}{8}\times 3 as a single fraction.

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

Fraction \frac{-3}{8} can be rewritten as -\frac{3}{8} by extracting the negative sign.

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

Divide 9y by 6 to get \frac{3}{2}y.

$$-\frac{3}{8}x+\frac{3}{2}y$$

Factor

$$\frac{3\left(4y-x\right)}{8}$$

Solution Steps

Factor out \frac{1}{24}.

$$\frac{9x+20y-18x+16y}{24}$$

Consider 9x+20y-18x+16y. Multiply and combine like terms.

$$-9x+36y$$

Consider -9x+36y. Factor out 9.

$$9\left(-x+4y\right)$$

Rewrite the complete factored expression.

$$\frac{3\left(-x+4y\right)}{8}$$