Peform each indicated operation by using LCD and simplify the result. Can you please show me the steps on how you got the answer because I don't understand how to these problems. Thank you.

y+2 over y^2+2y+4 + 1 over y-2

z-3 over z^2+z-6 + 2z+1 over z-2

To perform these operations using the Least Common Denominator (LCD) and simplify the result, follow these steps:

1. Identify the denominators in each expression:
- For the first expression, the denominators are y^2+2y+4 and y-2.
- For the second expression, the denominators are z^2+z-6 and z-2.

2. Find the LCD for each expression by factoring the denominators:
- For the first expression, y^2+2y+4 can be factored as (y+2)(y+2), and y-2 remains the same. So the LCD for the first expression is (y+2)(y+2)(y-2).
- For the second expression, z^2+z-6 can be factored as (z+3)(z-2), and z-2 remains the same. So the LCD for the second expression is (z+3)(z-2)(z-2).

3. Rewrite each expression with the LCD:
- For the first expression, we need to multiply each term by the missing factors in the LCD:
(y+2) / (y^2+2y+4) + 1 / (y-2) = [(y+2) * (y-2)] / [(y+2)(y+2)(y-2)] + [(y+2)(y+2)] / [(y+2)(y+2)(y-2)].

- For the second expression, we need to multiply each term by the missing factors in the LCD:
(z-3) / (z^2+z-6) + (2z+1) / (z-2) = [(z-3) * (z+3)] / [(z+3)(z-2)(z-2)] + [(2z+1) * (z-2)] / [(z+3)(z-2)(z-2)].

4. Simplify the numerators:
- For the first expression, multiplying the numerators gives:
(y+2) * (y-2) = y^2 - 4.

- For the second expression, multiplying the numerators gives:
(z-3) * (z+3) = z^2 - 9.

5. Rewrite the expressions with the simplified numerators:
- For the first expression, we have:
(y^2 - 4) / [(y+2)(y+2)(y-2)] + [(y+2)(y+2)] / [(y+2)(y+2)(y-2)].

- For the second expression, we have:
(z^2 - 9) / [(z+3)(z-2)(z-2)] + [(2z+1) * (z-2)] / [(z+3)(z-2)(z-2)].

6. Combine the numerators over the LCD:
- For the first expression, add the two terms with the common denominator:
(y^2 - 4 + (y+2)(y+2)) / [(y+2)(y+2)(y-2)].

- For the second expression, add the two terms with the common denominator:
(z^2 - 9 + (2z+1) * (z-2)) / [(z+3)(z-2)(z-2)].

7. Simplify the numerators further if possible.

That's the general method for performing these operations using the LCD and simplifying the results.