Question

Simplify the expression. $$\frac{x^{2}+1}{x^{2}-4}+\frac{5 x}{x^{2}-4}-\frac{2 x+11}{x^{2}-4}$$

Short answer

\(\frac{x^{2}+3x-10}{x^{2}-4}\)

Step-by-step solution

Combine Like Terms

Since fractions can be added and subtracted if they have the same denominator, start by combining the numerators: \[(x^{2}+1)+(5x)-(2x+11)\]

Simplification

The expression simplifies to: \[x^{2}+5x-2x+1-11\] which further simplifies to: \[x^{2}+3x-10\]. The denominator remains the same.

Final Answer

Therefore, the simplified rational expression is \[\frac{x^{2}+3x-10}{x^{2}-4}\].