Solve y+2/4y^2-y-2/12y

$$\frac { y + 2 } { 4 y ^ { 2 } } - \frac { y - 2 } { 12 y }$$

Evaluate

$$-\frac{\left(y-6\right)\left(y+1\right)}{12y^{2}}$$

Short Solution Steps

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

$$\frac{3\left(y+2\right)}{12y^{2}}-\frac{\left(y-2\right)y}{12y^{2}}$$

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

$$\frac{3\left(y+2\right)-\left(y-2\right)y}{12y^{2}}$$

Do the multiplications in 3\left(y+2\right)-\left(y-2\right)y.

$$\frac{3y+6-y^{2}+2y}{12y^{2}}$$

Combine like terms in 3y+6-y^{2}+2y.

$$\frac{5y+6-y^{2}}{12y^{2}}$$

Expand

$$-\frac{1}{12}+\frac{5}{12y}+\frac{1}{2y^{2}}$$

Short Solution Steps

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

$$\frac{3\left(y+2\right)}{12y^{2}}-\frac{\left(y-2\right)y}{12y^{2}}$$

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

$$\frac{3\left(y+2\right)-\left(y-2\right)y}{12y^{2}}$$

Do the multiplications in 3\left(y+2\right)-\left(y-2\right)y.

$$\frac{3y+6-y^{2}+2y}{12y^{2}}$$

Combine like terms in 3y+6-y^{2}+2y.

$$\frac{5y+6-y^{2}}{12y^{2}}$$