Guía de problemas de funciones cuadráticas

Resolver los siguientes ejercicios

Problema n° 1) Resolver las siguientes ecuaciones fraccionarias de segundo grado:

1. (x + 2)/(x - 3) = (3·x - 4)/(x + 2)
2. (2·x - 2)/(x - 3) = (x + 2)/(x - 4)
3. (x + 1)/(x + 3) + (x - 3)/(x - 1) = 5/4
4. (x + 1)/(x + 2)² + 3·x/(x + 2) = ¼
5. [(x + 1)/(x - 1)]² + (x + 1)/(x - 1) - 6 = 0
6. 5/(x + 1)² + 4/(x - 1) = 1
7. (x² - 1)/(x - 2) + 5 = 3/(x - 2)
8. 3/(x - 2) + 2/(x - 3) = 2/(x - 4)
9. x/6 + 6/x = 6
10. 6/(x - 1) + 2/(x - 2) = 3/(x - 3)
11. 4/(x + 4) + 1/(x + 3) + 3/(x + 1) = 0
12. 6/(x + 2) - 3/(x² - x - 6) = 20/(9 - x²)
13. 4/(x² - x - 2) + 2/(x + 1) = 7,5/(x² - 4)
14. (x² + x + 3)/(x² - x + 3) = (2·x + 5)/(2·x + 7)
15. 3·x/(2·x + 1) = (x + 5)/(x + 1) + (x - 19)/(2·x² + 3·x + 1)
16. (5·x - 2)/(2·x + 2) + (3·x + 2)/(4·x - 4) = 5·x/(x² - 1) + 15/7

Problema n° 2) Resolver:

Problema n° 3) Determinar k de modo que cada ecuación tenga sus raíces iguales:

1. x² - 5·x + k = 0
2. 3·x² + 8·x + k = 0
3. 2·x² - 6·x + k = 0
4. 25·x² + k·x + 1 = 0
5. k·x² + k·x + 1 = 0
6. k·x² - 3·x + k = 0