Guía de problemas de funciones cuadráticas.

Resolver los siguientes ejercicios:

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

a- (x + 2)/(x - 3) = (3·x - 4)/(x + 2)

b- (2·x - 2)/(x - 3) = (x + 2)/(x - 4)

c- (x + 1)/(x + 3) + (x - 3)/(x - 1) = 5/4

d- (x + 1)/(x + 2)² + 3·x/(x + 2) = ¼

e- [(x + 1)/(x - 1)]² + (x + 1)/(x - 1) - 6 = 0

f- 5/(x + 1)² + 4/(x - 1) = 1

g- (x² - 1)/(x - 2) + 5 = 3/(x - 2)

h- 3/(x - 2) + 2/(x - 3) = 2/(x - 4)

i- x/6 + 6/x = 6

j- 6/(x - 1) + 2/(x - 2) = 3/(x - 3)

k- 4/(x + 4) + 1/(x + 3) + 3/(x + 1) = 0

l- 6/(x + 2) - 3/(x² - x - 6) = 20/(9 - x²)

m- 4/(x² - x - 2) + 2/(x + 1) = 7,5/(x² - 4)

n- (x² + x + 3)/(x² - x + 3) = (2·x + 5)/(2·x + 7)

o- 3·x/(2·x + 1) = (x + 5)/(x + 1) + (x - 19)/(2·x² + 3·x + 1)

p- (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:

a) x² - 5·x + k = 0

b) 3·x² + 8·x + k = 0

c) 2·x² - 6·x + k = 0

d) 25·x² + k·x + 1 = 0

e) k·x² + k·x + 1 = 0

f) k·x² - 3·x + k = 0