Resposta:

a)

x+1/x=5/2

tudo vezes 2x

2x²+2=5x

2x²-5x+2=0

x'=[5+√(25-16)]/4=(5+3)/4=2

x''=[5-√(25-16)]/4=(5-3)/4=1/2

b)

x/3-9/x=-2

tudo vezes 3x

x²-27=-6x

x²+6x-27=0

x'=[-6+√(36+108)]/2=(-6+12)/2=3

x''=[-6-√(36+108)]/2=(-6-12)/2=-9

c)

x+3/(x-2)=6

tudo vezes (x-2)

x*(x-2)+3=6*(x-2)

x²-2x+3=6x-12

x²-8x+15=0

x'=[8+√(64-60)]/2=(8+2)/2=5

x''=[8-√(64-60)]/2=(8-2)/2=3

d)

x+1/(x-4)=6

tudo vezes x-4

x*(x-4)+1=6*(x-4)

x²-4x+1=6x-24

x²-10x+25=0

(x-5)²=0

x-5=0

x=5

e)

x+1/(x-5)=7

tudo vezes (x-5)

x*(x-5)+1=7(x-5)

x²-5x+1=7x-35

x²-12x+36=0

(x-6)²=0

x-6=0

x=6

f)

1/x+5/x²-6=0

tudo vezes x²

x²/x +5x²/x²=6x²

x+5=6x²

6x²-x-5=0

x'=[1+√(1+120)]/12=(1+11)/12=1

x''=[1-√(1+120)]/12=(1-11)/12=-10/12=-5/6