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  • Usuário do Brainly
2014-08-15T18:04:29-03:00
Primeira figura:

a) \dfrac{4}{1-x}-\dfrac{5}{x+1}=\dfrac{3x-2}{1-x^2}.

\dfrac{4(x+1)}{(1-x)(x+1)}-\dfrac{5(1-x)}{(1-x)(x+1)}=\dfrac{3x-2}{(1-x)(x+1)}

4(x+1)-5(1-x)=3x-2

4x+4-5+5x=3x-2

4x+5x-3x=5-4-2

6x=-1

x=\dfrac{-1}{6}


b) \dfrac{1}{x+4}+\dfrac{1}{x-4}=\dfrac{-8}{x^2-16}

\dfrac{(x-4)+(x+4)}{(x+4)(x-4)}=\dfrac{-8}{(x+4)(x-4)}

(x-4)+(x+4)=-8

2x=-8

x=-4

Mas, note que, se x=-4 o denominador da primeira fração será zero.

Portanto, esta equação não possui solução.

c) \dfrac{1}{x}+\dfrac{1}{x-2}-\dfrac{2}{x+2}=\dfrac{3}{x^2-4}

\dfrac{(x-2)(x+2)+x(x+2)-2x(x-2)}{x(x-2)(x+2)}=\dfrac{3}{(x-2)(x+2)}

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

x^2-4+x^2+2x-2x^2+4x=3x

6x-4=3x

3x=4

x=\dfrac{4}{3}

d) \dfrac{3}{x}+\dfrac{1}{x-1}=\dfrac{-3x+4}{x^2-x}

\dfrac{3(x-1)+x}{x(x-1)}=\dfrac{-3x+4}{x(x-1)}

3(x-1)+x=-3x+4

3x-3+x=-3x+4

3x+x+3x=4+3

7x=7

x=1.


Segunda figura:

a) \dfrac{x-1}{a+1}+\dfrac{x+1}{a+3}=2

\dfrac{(x-1)(a+3)+(x+1)(a+1)}{(a+1)(a+3)}=2

ax+3x-a-3+ax+x+a+1=2(a+1)(a+3)

x(a+3+a+1)=2(a+1)(a+3)+8

x(2a+4)=(2a+4)(a+2)

x=\dfrac{(2a+4)(a+2)}{(2a+4)}=a+2


b) a^2x+10a+25x+a^2+25 

a^2x-25x=a^2-10a+25

x(a^2-25)=(a-5)^2

x(a-5)(a+5)=(a-5)(a-5)

x=\dfrac{(a-5)(a-5)}{(a-5)(a+5)}=\dfrac{a-5}{a+5}.


c) \dfrac{a}{x+a}+\dfrac{ax}{x^2-a^2}=\dfrac{a}{x-a}.

\dfrac{a(x-a)+ax}{(x+a)(x-a)}=\dfrac{a}{x-a}

a(x-a)+ax=a(x+a)

ax-a^2+ax=ax+a^2

ax=2a^2

x=\dfrac{2a^2}{a}=2a


Terceira figura:

\dfrac{210}{x}=\dfrac{120}{x-3}

210(x-3)=120x

210x-120x=210\cdot3

90x=630

x=\dfrac{630}{90}=7

Quarta figura:

\dfrac{360}{x}=\dfrac{270}{x-2}

360(x-2)=270x

360x-270x=360\cdot2

90x=720

x=\dfrac{720}{90}=8
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