Solve 3/6y(y+8)+y-5/y^2(y-3)

$$\frac { 3 } { 6 y ( y + 8 ) } + \frac { y - 5 } { y ^ { 2 } ( y - 3 ) }$$

Evaluate

$$\frac{3y^{2}+3y-80}{2\left(y-3\right)\left(y+8\right)y^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 6y\left(y+8\right) and y^{2}\left(y-3\right) is 6\left(y-3\right)\left(y+8\right)y^{2}. Multiply \frac{3}{6y\left(y+8\right)} times \frac{y\left(y-3\right)}{y\left(y-3\right)}. Multiply \frac{y-5}{y^{2}\left(y-3\right)} times \frac{6\left(y+8\right)}{6\left(y+8\right)}.

$$\frac{3y\left(y-3\right)}{6\left(y-3\right)\left(y+8\right)y^{2}}+\frac{\left(y-5\right)\times 6\left(y+8\right)}{6\left(y-3\right)\left(y+8\right)y^{2}}$$

Since \frac{3y\left(y-3\right)}{6\left(y-3\right)\left(y+8\right)y^{2}} and \frac{\left(y-5\right)\times 6\left(y+8\right)}{6\left(y-3\right)\left(y+8\right)y^{2}} have the same denominator, add them by adding their numerators.

$$\frac{3y\left(y-3\right)+\left(y-5\right)\times 6\left(y+8\right)}{6\left(y-3\right)\left(y+8\right)y^{2}}$$

Do the multiplications in 3y\left(y-3\right)+\left(y-5\right)\times 6\left(y+8\right).

$$\frac{3y^{2}-9y+6y^{2}+48y-30y-240}{6\left(y-3\right)\left(y+8\right)y^{2}}$$

Combine like terms in 3y^{2}-9y+6y^{2}+48y-30y-240.

$$\frac{9y^{2}+9y-240}{6\left(y-3\right)\left(y+8\right)y^{2}}$$

Expand 6\left(y-3\right)\left(y+8\right)y^{2}.

$$\frac{9y^{2}+9y-240}{6y^{4}+30y^{3}-144y^{2}}$$

Expand

$$\frac{3y^{2}+3y-80}{2\left(y-3\right)\left(y+8\right)y^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 6y\left(y+8\right) and y^{2}\left(y-3\right) is 6\left(y-3\right)\left(y+8\right)y^{2}. Multiply \frac{3}{6y\left(y+8\right)} times \frac{y\left(y-3\right)}{y\left(y-3\right)}. Multiply \frac{y-5}{y^{2}\left(y-3\right)} times \frac{6\left(y+8\right)}{6\left(y+8\right)}.

$$\frac{3y\left(y-3\right)}{6\left(y-3\right)\left(y+8\right)y^{2}}+\frac{\left(y-5\right)\times 6\left(y+8\right)}{6\left(y-3\right)\left(y+8\right)y^{2}}$$

Since \frac{3y\left(y-3\right)}{6\left(y-3\right)\left(y+8\right)y^{2}} and \frac{\left(y-5\right)\times 6\left(y+8\right)}{6\left(y-3\right)\left(y+8\right)y^{2}} have the same denominator, add them by adding their numerators.

$$\frac{3y\left(y-3\right)+\left(y-5\right)\times 6\left(y+8\right)}{6\left(y-3\right)\left(y+8\right)y^{2}}$$

Do the multiplications in 3y\left(y-3\right)+\left(y-5\right)\times 6\left(y+8\right).

$$\frac{3y^{2}-9y+6y^{2}+48y-30y-240}{6\left(y-3\right)\left(y+8\right)y^{2}}$$

Combine like terms in 3y^{2}-9y+6y^{2}+48y-30y-240.

$$\frac{9y^{2}+9y-240}{6\left(y-3\right)\left(y+8\right)y^{2}}$$

Expand 6\left(y-3\right)\left(y+8\right)y^{2}.

$$\frac{9y^{2}+9y-240}{6y^{4}+30y^{3}-144y^{2}}$$