Question

(5/x-2)-(x+13/x^2-x-2)

Answer 1

Вот решение твоего примера

Answer 2

To simplify the expression $\frac{5}{x-2}-\frac{x+13}{x^2-x-2}$, we'll first factor the denominators and then combine the fractions:

1. Factor the denominators:

   $$x-2 = x - 2$$
   $$x^2-x-2 = (x-2)(x+1)$$

2. Rewrite the fractions with the common denominator $(x-2)(x+1)$:

   $$\frac{5}{x-2} - \frac{x+13}{x^2-x-2} = \frac{5}{x-2} - \frac{x+13}{(x-2)(x+1)}$$

3. Now, let's find a common denominator and combine the fractions:

   $$\frac{5(x+1)}{(x-2)(x+1)} - \frac{x+13}{(x-2)(x+1)}$$

4. Combine the fractions:

   $$\frac{5(x+1) - (x+13)}{(x-2)(x+1)}$$

5. Distribute and simplify the numerator:

   $$\frac{5x+5 - x - 13}{(x-2)(x+1)} = \frac{4x - 8}{(x-2)(x+1)}$$

6. Factor out a common term from the numerator:

   $$\frac{4(x - 2)}{(x-2)(x+1)}$$

7. Cancel out the common factor of $x-2$:

   $$\frac{4}{x+1}$$

So, the simplified expression is $\frac{4}{x+1}$.