Solve 3x-5y/y+7/3x+5y

$$\frac { 3 x - 5 y } { y } + \frac { 7 } { 3 x + 5 y }$$

Evaluate

$$\frac{9x^{2}-25y^{2}+7y}{y\left(3x+5y\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of y and 3x+5y is y\left(3x+5y\right). Multiply \frac{3x-5y}{y} times \frac{3x+5y}{3x+5y}. Multiply \frac{7}{3x+5y} times \frac{y}{y}.

$$\frac{\left(3x-5y\right)\left(3x+5y\right)}{y\left(3x+5y\right)}+\frac{7y}{y\left(3x+5y\right)}$$

Since \frac{\left(3x-5y\right)\left(3x+5y\right)}{y\left(3x+5y\right)} and \frac{7y}{y\left(3x+5y\right)} have the same denominator, add them by adding their numerators.

$$\frac{\left(3x-5y\right)\left(3x+5y\right)+7y}{y\left(3x+5y\right)}$$

Do the multiplications in \left(3x-5y\right)\left(3x+5y\right)+7y.

$$\frac{9x^{2}+15xy-15yx-25y^{2}+7y}{y\left(3x+5y\right)}$$

Combine like terms in 9x^{2}+15xy-15yx-25y^{2}+7y.

$$\frac{9x^{2}-25y^{2}+7y}{y\left(3x+5y\right)}$$

Expand y\left(3x+5y\right).

$$\frac{9x^{2}-25y^{2}+7y}{3xy+5y^{2}}$$

Expand

$$\frac{9x^{2}-25y^{2}+7y}{y\left(3x+5y\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of y and 3x+5y is y\left(3x+5y\right). Multiply \frac{3x-5y}{y} times \frac{3x+5y}{3x+5y}. Multiply \frac{7}{3x+5y} times \frac{y}{y}.

$$\frac{\left(3x-5y\right)\left(3x+5y\right)}{y\left(3x+5y\right)}+\frac{7y}{y\left(3x+5y\right)}$$

Since \frac{\left(3x-5y\right)\left(3x+5y\right)}{y\left(3x+5y\right)} and \frac{7y}{y\left(3x+5y\right)} have the same denominator, add them by adding their numerators.

$$\frac{\left(3x-5y\right)\left(3x+5y\right)+7y}{y\left(3x+5y\right)}$$

Do the multiplications in \left(3x-5y\right)\left(3x+5y\right)+7y.

$$\frac{9x^{2}+15xy-15yx-25y^{2}+7y}{y\left(3x+5y\right)}$$

Combine like terms in 9x^{2}+15xy-15yx-25y^{2}+7y.

$$\frac{9x^{2}-25y^{2}+7y}{y\left(3x+5y\right)}$$

Expand y\left(3x+5y\right).

$$\frac{9x^{2}-25y^{2}+7y}{3xy+5y^{2}}$$