Solve 5/4y(y+2)+y-6/y^2(y-1)

$$\frac { 5 } { 4 y ( y + 2 ) } + \frac { y - 6 } { y ^ { 2 } ( y - 1 ) }$$

Evaluate

$$\frac{3\left(3y^{2}-7y-16\right)}{4\left(y-1\right)\left(y+2\right)y^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4y\left(y+2\right) and y^{2}\left(y-1\right) is 4\left(y-1\right)\left(y+2\right)y^{2}. Multiply \frac{5}{4y\left(y+2\right)} times \frac{y\left(y-1\right)}{y\left(y-1\right)}. Multiply \frac{y-6}{y^{2}\left(y-1\right)} times \frac{4\left(y+2\right)}{4\left(y+2\right)}.

$$\frac{5y\left(y-1\right)}{4\left(y-1\right)\left(y+2\right)y^{2}}+\frac{\left(y-6\right)\times 4\left(y+2\right)}{4\left(y-1\right)\left(y+2\right)y^{2}}$$

Since \frac{5y\left(y-1\right)}{4\left(y-1\right)\left(y+2\right)y^{2}} and \frac{\left(y-6\right)\times 4\left(y+2\right)}{4\left(y-1\right)\left(y+2\right)y^{2}} have the same denominator, add them by adding their numerators.

$$\frac{5y\left(y-1\right)+\left(y-6\right)\times 4\left(y+2\right)}{4\left(y-1\right)\left(y+2\right)y^{2}}$$

Do the multiplications in 5y\left(y-1\right)+\left(y-6\right)\times 4\left(y+2\right).

$$\frac{5y^{2}-5y+4y^{2}+8y-24y-48}{4\left(y-1\right)\left(y+2\right)y^{2}}$$

Combine like terms in 5y^{2}-5y+4y^{2}+8y-24y-48.

$$\frac{9y^{2}-21y-48}{4\left(y-1\right)\left(y+2\right)y^{2}}$$

Expand 4\left(y-1\right)\left(y+2\right)y^{2}.

$$\frac{9y^{2}-21y-48}{4y^{4}+4y^{3}-8y^{2}}$$

Expand

$$\frac{3\left(3y^{2}-7y-16\right)}{4\left(y-1\right)\left(y+2\right)y^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4y\left(y+2\right) and y^{2}\left(y-1\right) is 4\left(y-1\right)\left(y+2\right)y^{2}. Multiply \frac{5}{4y\left(y+2\right)} times \frac{y\left(y-1\right)}{y\left(y-1\right)}. Multiply \frac{y-6}{y^{2}\left(y-1\right)} times \frac{4\left(y+2\right)}{4\left(y+2\right)}.

$$\frac{5y\left(y-1\right)}{4\left(y-1\right)\left(y+2\right)y^{2}}+\frac{\left(y-6\right)\times 4\left(y+2\right)}{4\left(y-1\right)\left(y+2\right)y^{2}}$$

Since \frac{5y\left(y-1\right)}{4\left(y-1\right)\left(y+2\right)y^{2}} and \frac{\left(y-6\right)\times 4\left(y+2\right)}{4\left(y-1\right)\left(y+2\right)y^{2}} have the same denominator, add them by adding their numerators.

$$\frac{5y\left(y-1\right)+\left(y-6\right)\times 4\left(y+2\right)}{4\left(y-1\right)\left(y+2\right)y^{2}}$$

Do the multiplications in 5y\left(y-1\right)+\left(y-6\right)\times 4\left(y+2\right).

$$\frac{5y^{2}-5y+4y^{2}+8y-24y-48}{4\left(y-1\right)\left(y+2\right)y^{2}}$$

Combine like terms in 5y^{2}-5y+4y^{2}+8y-24y-48.

$$\frac{9y^{2}-21y-48}{4\left(y-1\right)\left(y+2\right)y^{2}}$$

Expand 4\left(y-1\right)\left(y+2\right)y^{2}.

$$\frac{9y^{2}-21y-48}{4y^{4}+4y^{3}-8y^{2}}$$