Solve 1/y+2/7-3/2{y_{2}}

$$\frac{ 1 }{ y } + \frac{ 2 }{ 7 } - \frac{ 3 }{ 2 { y }_{ 2 } }$$

Evaluate

$$\frac{4yy_{2}-21y+14y_{2}}{14yy_{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of y and 7 is 7y. Multiply \frac{1}{y} times \frac{7}{7}. Multiply \frac{2}{7} times \frac{y}{y}.

$$\frac{7}{7y}+\frac{2y}{7y}-\frac{3}{2y_{2}}$$

Since \frac{7}{7y} and \frac{2y}{7y} have the same denominator, add them by adding their numerators.

$$\frac{7+2y}{7y}-\frac{3}{2y_{2}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 7y and 2y_{2} is 14yy_{2}. Multiply \frac{7+2y}{7y} times \frac{2y_{2}}{2y_{2}}. Multiply \frac{3}{2y_{2}} times \frac{7y}{7y}.

$$\frac{\left(7+2y\right)\times 2y_{2}}{14yy_{2}}-\frac{3\times 7y}{14yy_{2}}$$

Since \frac{\left(7+2y\right)\times 2y_{2}}{14yy_{2}} and \frac{3\times 7y}{14yy_{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(7+2y\right)\times 2y_{2}-3\times 7y}{14yy_{2}}$$

Do the multiplications in \left(7+2y\right)\times 2y_{2}-3\times 7y.

$$\frac{14y_{2}+4yy_{2}-21y}{14yy_{2}}$$

Factor

$$\frac{\left(4-\frac{21}{y_{2}}\right)y+14}{14y}$$