Question

1. simplify \\(\frac{5x}{x + 2}+\frac{x + 3}{x - 2}\\)

Explanation:

Step1: Find common denominator

The common denominator of $\frac{5x}{x+2}$ and $\frac{x+3}{x-2}$ is $(x+2)(x-2) = x^2 - 4$.

Step2: Rewrite fractions with common denominator

$$\frac{5x(x-2)}{(x+2)(x-2)} + \frac{(x+3)(x+2)}{(x+2)(x-2)}$$

Step3: Expand numerators

$$\frac{5x^2 - 10x + x^2 + 5x + 6}{x^2 - 4}$$

Step4: Combine like terms in numerator

$$\frac{(5x^2+x^2)+(-10x+5x)+6}{x^2 - 4} = \frac{6x^2 - 5x + 6}{x^2 - 4}$$

Answer:

$\frac{6x^2 - 5x + 6}{x^2 - 4}$