Solve x/3+2x/3-y/5+6y/5-frac{4x}{3}+frac{10x}{7}

$$\frac { x } { 3 } + \frac { 2 x } { 3 } - \frac { y } { 5 } + \frac { 6 y } { 5 } - \frac { 4 x } { 3 } + \frac { 10 x } { 7 }$$

Evaluate

$$\frac{23x}{21}+y$$

Short Solution Steps

Since \frac{x}{3} and \frac{2x}{3} have the same denominator, add them by adding their numerators.

$$\frac{x+2x}{3}-\frac{y}{5}+\frac{6y}{5}-\frac{4x}{3}+\frac{10x}{7}$$

Combine like terms in x+2x.

$$\frac{3x}{3}-\frac{y}{5}+\frac{6y}{5}-\frac{4x}{3}+\frac{10x}{7}$$

Cancel out 3 and 3.

$$x-\frac{y}{5}+\frac{6y}{5}-\frac{4x}{3}+\frac{10x}{7}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{5}{5}.

$$\frac{5x}{5}-\frac{y}{5}+\frac{6y}{5}-\frac{4x}{3}+\frac{10x}{7}$$

Since \frac{5x}{5} and \frac{y}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5x-y}{5}+\frac{6y}{5}-\frac{4x}{3}+\frac{10x}{7}$$

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

$$\frac{5x-y+6y}{5}-\frac{4x}{3}+\frac{10x}{7}$$

Combine like terms in 5x-y+6y.

$$\frac{5x+5y}{5}-\frac{4x}{3}+\frac{10x}{7}$$

Divide each term of 5x+5y by 5 to get x+y.

$$x+y-\frac{4x}{3}+\frac{10x}{7}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x+y times \frac{3}{3}.

$$\frac{3\left(x+y\right)}{3}-\frac{4x}{3}+\frac{10x}{7}$$

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

$$\frac{3\left(x+y\right)-4x}{3}+\frac{10x}{7}$$

Do the multiplications in 3\left(x+y\right)-4x.

$$\frac{3x+3y-4x}{3}+\frac{10x}{7}$$

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

$$\frac{-x+3y}{3}+\frac{10x}{7}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 7 is 21. Multiply \frac{-x+3y}{3} times \frac{7}{7}. Multiply \frac{10x}{7} times \frac{3}{3}.

$$\frac{7\left(-x+3y\right)}{21}+\frac{3\times 10x}{21}$$

Since \frac{7\left(-x+3y\right)}{21} and \frac{3\times 10x}{21} have the same denominator, add them by adding their numerators.

$$\frac{7\left(-x+3y\right)+3\times 10x}{21}$$

Do the multiplications in 7\left(-x+3y\right)+3\times 10x.

$$\frac{-7x+21y+30x}{21}$$

Combine like terms in -7x+21y+30x.

$$\frac{23x+21y}{21}$$

Factor

$$\frac{23x+21y}{21}$$

Solution Steps

Factor out \frac{1}{105}.

$$\frac{35x+70x-21y+126y-140x+150x}{105}$$

Consider 35x+70x-21y+126y-140x+150x. Multiply and combine like terms.

$$115x+105y$$

Consider 115x+105y. Factor out 5.

$$5\left(23x+21y\right)$$

Rewrite the complete factored expression.

$$\frac{23x+21y}{21}$$