Solve 8y/y-9-y+9/8y

$$\frac{ 8y }{ y-9 } - \frac{ y+9 }{ 8y }$$

Evaluate

$$\frac{9\left(7y^{2}+9\right)}{8y\left(y-9\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of y-9 and 8y is 8y\left(y-9\right). Multiply \frac{8y}{y-9} times \frac{8y}{8y}. Multiply \frac{y+9}{8y} times \frac{y-9}{y-9}.

$$\frac{8y\times 8y}{8y\left(y-9\right)}-\frac{\left(y+9\right)\left(y-9\right)}{8y\left(y-9\right)}$$

Since \frac{8y\times 8y}{8y\left(y-9\right)} and \frac{\left(y+9\right)\left(y-9\right)}{8y\left(y-9\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8y\times 8y-\left(y+9\right)\left(y-9\right)}{8y\left(y-9\right)}$$

Do the multiplications in 8y\times 8y-\left(y+9\right)\left(y-9\right).

$$\frac{64y^{2}-y^{2}+9y-9y+81}{8y\left(y-9\right)}$$

Combine like terms in 64y^{2}-y^{2}+9y-9y+81.

$$\frac{63y^{2}+81}{8y\left(y-9\right)}$$

Expand 8y\left(y-9\right).

$$\frac{63y^{2}+81}{8y^{2}-72y}$$

Expand

$$\frac{9\left(7y^{2}+9\right)}{8y\left(y-9\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of y-9 and 8y is 8y\left(y-9\right). Multiply \frac{8y}{y-9} times \frac{8y}{8y}. Multiply \frac{y+9}{8y} times \frac{y-9}{y-9}.

$$\frac{8y\times 8y}{8y\left(y-9\right)}-\frac{\left(y+9\right)\left(y-9\right)}{8y\left(y-9\right)}$$

Since \frac{8y\times 8y}{8y\left(y-9\right)} and \frac{\left(y+9\right)\left(y-9\right)}{8y\left(y-9\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8y\times 8y-\left(y+9\right)\left(y-9\right)}{8y\left(y-9\right)}$$

Do the multiplications in 8y\times 8y-\left(y+9\right)\left(y-9\right).

$$\frac{64y^{2}-y^{2}+9y-9y+81}{8y\left(y-9\right)}$$

Combine like terms in 64y^{2}-y^{2}+9y-9y+81.

$$\frac{63y^{2}+81}{8y\left(y-9\right)}$$

Expand 8y\left(y-9\right).

$$\frac{63y^{2}+81}{8y^{2}-72y}$$