Solve 9/(2x-10)+x/x^2-25

$$\frac { 9 } { ( 2 x - 10 ) } + \frac { x } { x ^ { 2 } - 25 }$$

Evaluate

$$\frac{11x+45}{2\left(x^{2}-25\right)}$$

Short Solution Steps

Factor 2x-10. Factor x^{2}-25.

$$\frac{9}{2\left(x-5\right)}+\frac{x}{\left(x-5\right)\left(x+5\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2\left(x-5\right) and \left(x-5\right)\left(x+5\right) is 2\left(x-5\right)\left(x+5\right). Multiply \frac{9}{2\left(x-5\right)} times \frac{x+5}{x+5}. Multiply \frac{x}{\left(x-5\right)\left(x+5\right)} times \frac{2}{2}.

$$\frac{9\left(x+5\right)}{2\left(x-5\right)\left(x+5\right)}+\frac{2x}{2\left(x-5\right)\left(x+5\right)}$$

Since \frac{9\left(x+5\right)}{2\left(x-5\right)\left(x+5\right)} and \frac{2x}{2\left(x-5\right)\left(x+5\right)} have the same denominator, add them by adding their numerators.

$$\frac{9\left(x+5\right)+2x}{2\left(x-5\right)\left(x+5\right)}$$

Do the multiplications in 9\left(x+5\right)+2x.

$$\frac{9x+45+2x}{2\left(x-5\right)\left(x+5\right)}$$

Combine like terms in 9x+45+2x.

$$\frac{11x+45}{2\left(x-5\right)\left(x+5\right)}$$

Expand 2\left(x-5\right)\left(x+5\right).

$$\frac{11x+45}{2x^{2}-50}$$

Factor

$$\frac{11x+45}{2\left(x^{2}-25\right)}$$