Question

RELACIONE AS COLUNAS:

( )
$\frac{1}{x} + \frac{x}{1} = \frac{5}{2}$

( )
$\frac{1}{x - 2} = \frac{x + 2}{3}$

( )
$\frac{3}{2x} = \frac{1}{x + 1}$

( )
$\frac{x + 1}{x - 2} + \frac{1}{x + 3} = \frac{1}{2}$
__________________________

A ) ( 0, - 1 )

B ) ( -3, 2 )

C ) ( 0 )

D ) ( 2 )

Answer 1

Fazemos MMC de x e 1, e vai ser x , pois todo número é múltiplo de 1

$\frac{1+x^{2}}{x}=\frac{5}{2}\\\\ 1+x^{2}=\frac{5x}{2}\\\\ x^{2}-2.5x +1=0$

Δ=b²-4.a.c

Δ=6.25-4.1.1

Δ=2.25

$x=\frac{-b+-\sqrt{delta}}{2.a}\\\\ x`=\frac{2.5+1.5}{2}=2\\\\ x``=\frac{2.5-1.5}{2}=\frac{1}{2}=0,5$

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multiplique cruzado

$\frac{x}{x-2}=\frac{x+2}{3}  \\\\ x^{2}-4=3x\\\\ x^{2}-3x-4=0$

Δ=9-4.1.-4

Δ=25

x`=(3+5)/2=4

x``=(3-5)/2=-1

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multiplique cruzado também

3x+3=2x

3x-2x=-3

x=-3

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faz mmc=x²+x-6

$\frac{x^{2}+4x+3+x-2}{x^{2}+x-6}= \frac{1}{2}\\\\ \frac{x^{2}+5x+1}{x^2+x-6}=\frac{1}{2}\\\\ x^{2}+x-6=2x^{2}+10x+2\\\\ 2x^{2}-x^{2}+10x-x+2+6=0\\\\ x^{2}+9x+8=0$

Δ=81-4.1.8

Δ=49

x`=(-9+7)/2=-1

x``=(-9-7)/2=-8