Calculate: /(x) x+5+/(6 x-3) x-5

Expression: $$\frac { x } { x + 5 } + \frac { 6 x - 3 } { x - 5 }$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $x+5$ and $x-5$ is $\left(x-5\right)\left(x+5\right)$. Multiply $\frac{x}{x+5}$ times $\frac{x-5}{x-5}$. Multiply $\frac{6x-3}{x-5}$ times $\frac{x+5}{x+5}$.

$$\frac{x\left(x-5\right)}{\left(x-5\right)\left(x+5\right)}+\frac{\left(6x-3\right)\left(x+5\right)}{\left(x-5\right)\left(x+5\right)}$$

Since $\frac{x\left(x-5\right)}{\left(x-5\right)\left(x+5\right)}$ and $\frac{\left(6x-3\right)\left(x+5\right)}{\left(x-5\right)\left(x+5\right)}$ have the same denominator, add them by adding their numerators.

$$\frac{x\left(x-5\right)+\left(6x-3\right)\left(x+5\right)}{\left(x-5\right)\left(x+5\right)}$$

Do the multiplications in $x\left(x-5\right)+\left(6x-3\right)\left(x+5\right)$.

$$\frac{x^{2}-5x+6x^{2}+30x-3x-15}{\left(x-5\right)\left(x+5\right)}$$

Combine like terms in $x^{2}-5x+6x^{2}+30x-3x-15$.

$$\frac{22x-15+7x^{2}}{\left(x-5\right)\left(x+5\right)}$$

Expand $\left(x-5\right)\left(x+5\right)$.

$$\frac{22x-15+7x^{2}}{x^{2}-25}$$