Solve 4x-23y/4-4x-25y/6+19y-3x/12

$$\frac { 4 x - 23 y } { 4 } - \frac { 4 x - 25 y } { 6 } + \frac { 19 y - 3 x } { 12 }$$

Evaluate

$$\frac{x}{12}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and 6 is 12. Multiply \frac{4x-23y}{4} times \frac{3}{3}. Multiply \frac{4x-25y}{6} times \frac{2}{2}.

$$\frac{3\left(4x-23y\right)}{12}-\frac{2\left(4x-25y\right)}{12}+\frac{19y-3x}{12}$$

Since \frac{3\left(4x-23y\right)}{12} and \frac{2\left(4x-25y\right)}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3\left(4x-23y\right)-2\left(4x-25y\right)}{12}+\frac{19y-3x}{12}$$

Do the multiplications in 3\left(4x-23y\right)-2\left(4x-25y\right).

$$\frac{12x-69y-8x+50y}{12}+\frac{19y-3x}{12}$$

Combine like terms in 12x-69y-8x+50y.

$$\frac{4x-19y}{12}+\frac{19y-3x}{12}$$

Since \frac{4x-19y}{12} and \frac{19y-3x}{12} have the same denominator, add them by adding their numerators.

$$\frac{4x-19y+19y-3x}{12}$$

Combine like terms in 4x-19y+19y-3x.

$$\frac{x}{12}$$

Expand

$$\frac{x}{12}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and 6 is 12. Multiply \frac{4x-23y}{4} times \frac{3}{3}. Multiply \frac{4x-25y}{6} times \frac{2}{2}.

$$\frac{3\left(4x-23y\right)}{12}-\frac{2\left(4x-25y\right)}{12}+\frac{19y-3x}{12}$$

Since \frac{3\left(4x-23y\right)}{12} and \frac{2\left(4x-25y\right)}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3\left(4x-23y\right)-2\left(4x-25y\right)}{12}+\frac{19y-3x}{12}$$

Do the multiplications in 3\left(4x-23y\right)-2\left(4x-25y\right).

$$\frac{12x-69y-8x+50y}{12}+\frac{19y-3x}{12}$$

Combine like terms in 12x-69y-8x+50y.

$$\frac{4x-19y}{12}+\frac{19y-3x}{12}$$

Since \frac{4x-19y}{12} and \frac{19y-3x}{12} have the same denominator, add them by adding their numerators.

$$\frac{4x-19y+19y-3x}{12}$$

Combine like terms in 4x-19y+19y-3x.

$$\frac{x}{12}$$