Questions: Add. 2/(x-5) + 3/(x+4)

Solution Steps

We start with the two fractions given in the problem: \[ \frac{2}{x - 5} \quad \text{and} \quad \frac{3}{x + 4} \]

To add these fractions, we need a common denominator. The common denominator is \((x - 5)(x + 4)\).

We rewrite each fraction with the common denominator: \[ \frac{2}{x - 5} = \frac{2(x + 4)}{(x - 5)(x + 4)} = \frac{2x + 8}{(x - 5)(x + 4)} \] \[ \frac{3}{x + 4} = \frac{3(x - 5)}{(x - 5)(x + 4)} = \frac{3x - 15}{(x - 5)(x + 4)} \]

Now we can combine the numerators over the common denominator: \[ \frac{2x + 8 + 3x - 15}{(x - 5)(x + 4)} = \frac{5x - 7}{(x - 5)(x + 4)} \]

Final Answer