Solve 4(x-5)/7-[5(x-y)/6+7x-y/21]

$$\frac { 4 ( x - 5 ) } { 7 } - [ \frac { 5 ( x - y ) } { 6 } + \frac { 7 x - y } { 21 } ]$$

Evaluate

$$\frac{37y}{42}-\frac{25x}{42}-\frac{20}{7}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 6 and 21 is 42. Multiply \frac{5\left(x-y\right)}{6} times \frac{7}{7}. Multiply \frac{7x-y}{21} times \frac{2}{2}.

$$\frac{4\left(x-5\right)}{7}-\left(\frac{7\times 5\left(x-y\right)}{42}+\frac{2\left(7x-y\right)}{42}\right)$$

Since \frac{7\times 5\left(x-y\right)}{42} and \frac{2\left(7x-y\right)}{42} have the same denominator, add them by adding their numerators.

$$\frac{4\left(x-5\right)}{7}-\frac{7\times 5\left(x-y\right)+2\left(7x-y\right)}{42}$$

Do the multiplications in 7\times 5\left(x-y\right)+2\left(7x-y\right).

$$\frac{4\left(x-5\right)}{7}-\frac{35x-35y+14x-2y}{42}$$

Combine like terms in 35x-35y+14x-2y.

$$\frac{4\left(x-5\right)}{7}-\frac{49x-37y}{42}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 7 and 42 is 42. Multiply \frac{4\left(x-5\right)}{7} times \frac{6}{6}.

$$\frac{6\times 4\left(x-5\right)}{42}-\frac{49x-37y}{42}$$

Since \frac{6\times 4\left(x-5\right)}{42} and \frac{49x-37y}{42} have the same denominator, subtract them by subtracting their numerators.

$$\frac{6\times 4\left(x-5\right)-\left(49x-37y\right)}{42}$$

Do the multiplications in 6\times 4\left(x-5\right)-\left(49x-37y\right).

$$\frac{24x-120-49x+37y}{42}$$

Combine like terms in 24x-120-49x+37y.

$$\frac{-25x-120+37y}{42}$$

Expand

$$\frac{37y}{42}-\frac{25x}{42}-\frac{20}{7}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 6 and 21 is 42. Multiply \frac{5\left(x-y\right)}{6} times \frac{7}{7}. Multiply \frac{7x-y}{21} times \frac{2}{2}.

$$\frac{4\left(x-5\right)}{7}-\left(\frac{7\times 5\left(x-y\right)}{42}+\frac{2\left(7x-y\right)}{42}\right)$$

Since \frac{7\times 5\left(x-y\right)}{42} and \frac{2\left(7x-y\right)}{42} have the same denominator, add them by adding their numerators.

$$\frac{4\left(x-5\right)}{7}-\frac{7\times 5\left(x-y\right)+2\left(7x-y\right)}{42}$$

Do the multiplications in 7\times 5\left(x-y\right)+2\left(7x-y\right).

$$\frac{4\left(x-5\right)}{7}-\frac{35x-35y+14x-2y}{42}$$

Combine like terms in 35x-35y+14x-2y.

$$\frac{4\left(x-5\right)}{7}-\frac{49x-37y}{42}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 7 and 42 is 42. Multiply \frac{4\left(x-5\right)}{7} times \frac{6}{6}.

$$\frac{6\times 4\left(x-5\right)}{42}-\frac{49x-37y}{42}$$

Since \frac{6\times 4\left(x-5\right)}{42} and \frac{49x-37y}{42} have the same denominator, subtract them by subtracting their numerators.

$$\frac{6\times 4\left(x-5\right)-\left(49x-37y\right)}{42}$$

Do the multiplications in 6\times 4\left(x-5\right)-\left(49x-37y\right).

$$\frac{24x-120-49x+37y}{42}$$

Combine like terms in 24x-120-49x+37y.

$$\frac{-25x-120+37y}{42}$$