Solución a la desigualdad fraccionaria menor que 0

-1<(5m-2)/(2-3m)<1

Resolver (5m-2)/(2-3m)>-1 ① Y (5m- 2)/(2-3m)<1 ②

Solución ①

(5m-2)/(2-3m)+1>0

[ (5m-2)+(2-3m)]/(2-3m)>0

2m/(2-3m)>0

m/(3m-2) <0

0

Solución ②

(5m-2)/(2-3m)-1<0

[(5m-2)-(2-3m)]/(2-3m)<0

(8m-4)/(2-3m)<0

(2m-1)/(3m-2)>0

m<1/2 o m>2/3

En resumen, la solución a la desigualdad es : 0

Desigualdades básicas

①√((a?+b?)/2)≥(a+b)/2≥√ab≥2 / (1/a+1/b)

②√(ab)≤(a+b)/2

③a?+b?≥2ab

④ab≤(a+b)?/4

⑤||a|-|b |≤|a+b|≤|a|+|b|