Solve 7/2y(y+6)+y-4/y^2(y-5)

$$\frac { 7 } { 2 y ( y + 6 ) } + \frac { y - 4 } { y ^ { 2 } ( y - 5 ) }$$

Evaluate

$$\frac{9y^{2}-31y-48}{2\left(y-5\right)\left(y+6\right)y^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2y\left(y+6\right) and y^{2}\left(y-5\right) is 2\left(y-5\right)\left(y+6\right)y^{2}. Multiply \frac{7}{2y\left(y+6\right)} times \frac{y\left(y-5\right)}{y\left(y-5\right)}. Multiply \frac{y-4}{y^{2}\left(y-5\right)} times \frac{2\left(y+6\right)}{2\left(y+6\right)}.

$$\frac{7y\left(y-5\right)}{2\left(y-5\right)\left(y+6\right)y^{2}}+\frac{\left(y-4\right)\times 2\left(y+6\right)}{2\left(y-5\right)\left(y+6\right)y^{2}}$$

Since \frac{7y\left(y-5\right)}{2\left(y-5\right)\left(y+6\right)y^{2}} and \frac{\left(y-4\right)\times 2\left(y+6\right)}{2\left(y-5\right)\left(y+6\right)y^{2}} have the same denominator, add them by adding their numerators.

$$\frac{7y\left(y-5\right)+\left(y-4\right)\times 2\left(y+6\right)}{2\left(y-5\right)\left(y+6\right)y^{2}}$$

Do the multiplications in 7y\left(y-5\right)+\left(y-4\right)\times 2\left(y+6\right).

$$\frac{7y^{2}-35y+2y^{2}+12y-8y-48}{2\left(y-5\right)\left(y+6\right)y^{2}}$$

Combine like terms in 7y^{2}-35y+2y^{2}+12y-8y-48.

$$\frac{9y^{2}-31y-48}{2\left(y-5\right)\left(y+6\right)y^{2}}$$

Expand 2\left(y-5\right)\left(y+6\right)y^{2}.

$$\frac{9y^{2}-31y-48}{2y^{4}+2y^{3}-60y^{2}}$$

Expand

$$\frac{9y^{2}-31y-48}{2\left(y-5\right)\left(y+6\right)y^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2y\left(y+6\right) and y^{2}\left(y-5\right) is 2\left(y-5\right)\left(y+6\right)y^{2}. Multiply \frac{7}{2y\left(y+6\right)} times \frac{y\left(y-5\right)}{y\left(y-5\right)}. Multiply \frac{y-4}{y^{2}\left(y-5\right)} times \frac{2\left(y+6\right)}{2\left(y+6\right)}.

$$\frac{7y\left(y-5\right)}{2\left(y-5\right)\left(y+6\right)y^{2}}+\frac{\left(y-4\right)\times 2\left(y+6\right)}{2\left(y-5\right)\left(y+6\right)y^{2}}$$

Since \frac{7y\left(y-5\right)}{2\left(y-5\right)\left(y+6\right)y^{2}} and \frac{\left(y-4\right)\times 2\left(y+6\right)}{2\left(y-5\right)\left(y+6\right)y^{2}} have the same denominator, add them by adding their numerators.

$$\frac{7y\left(y-5\right)+\left(y-4\right)\times 2\left(y+6\right)}{2\left(y-5\right)\left(y+6\right)y^{2}}$$

Do the multiplications in 7y\left(y-5\right)+\left(y-4\right)\times 2\left(y+6\right).

$$\frac{7y^{2}-35y+2y^{2}+12y-8y-48}{2\left(y-5\right)\left(y+6\right)y^{2}}$$

Combine like terms in 7y^{2}-35y+2y^{2}+12y-8y-48.

$$\frac{9y^{2}-31y-48}{2\left(y-5\right)\left(y+6\right)y^{2}}$$

Expand 2\left(y-5\right)\left(y+6\right)y^{2}.

$$\frac{9y^{2}-31y-48}{2y^{4}+2y^{3}-60y^{2}}$$