Solve 5z/z+3-z-3/5z

$$\frac { 5 z } { z + 3 } - \frac { z - 3 } { 5 z }$$

Evaluate

$$\frac{3\left(8z^{2}+3\right)}{5z\left(z+3\right)}$$

Short Solution Steps

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

$$\frac{5z\times 5z}{5z\left(z+3\right)}-\frac{\left(z-3\right)\left(z+3\right)}{5z\left(z+3\right)}$$

Since \frac{5z\times 5z}{5z\left(z+3\right)} and \frac{\left(z-3\right)\left(z+3\right)}{5z\left(z+3\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5z\times 5z-\left(z-3\right)\left(z+3\right)}{5z\left(z+3\right)}$$

Do the multiplications in 5z\times 5z-\left(z-3\right)\left(z+3\right).

$$\frac{25z^{2}-z^{2}-3z+3z+9}{5z\left(z+3\right)}$$

Combine like terms in 25z^{2}-z^{2}-3z+3z+9.

$$\frac{24z^{2}+9}{5z\left(z+3\right)}$$

Expand 5z\left(z+3\right).

$$\frac{24z^{2}+9}{5z^{2}+15z}$$

Expand

$$\frac{3\left(8z^{2}+3\right)}{5z\left(z+3\right)}$$

Short Solution Steps

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

$$\frac{5z\times 5z}{5z\left(z+3\right)}-\frac{\left(z-3\right)\left(z+3\right)}{5z\left(z+3\right)}$$

Since \frac{5z\times 5z}{5z\left(z+3\right)} and \frac{\left(z-3\right)\left(z+3\right)}{5z\left(z+3\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5z\times 5z-\left(z-3\right)\left(z+3\right)}{5z\left(z+3\right)}$$

Do the multiplications in 5z\times 5z-\left(z-3\right)\left(z+3\right).

$$\frac{25z^{2}-z^{2}-3z+3z+9}{5z\left(z+3\right)}$$

Combine like terms in 25z^{2}-z^{2}-3z+3z+9.

$$\frac{24z^{2}+9}{5z\left(z+3\right)}$$

Expand 5z\left(z+3\right).

$$\frac{24z^{2}+9}{5z^{2}+15z}$$