Question

#7 Show work Check for solutions ( including extraneous solutions)

Answer 1

1/x+x/(x+2)=1

take LCM
$(x+2)+x^2/(x(x+2)=1$
x+2+x^2=x(x+2)
$x^2+x+2=x^2+2x$
x=2
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2)$1/(x-3)+1/(x+5)=x+1/x-3$

$x+5+x-3/(x+1)(x-3)=x+1/x-3$
$2x+2=(x+1)(x+5)$
$2x+2=x^2+5x+x+5$
$x^2+4x+3=0$
$x^2+3x+x+3=0$
(x+1)(x+3)=0
x= - 1, x= - 3

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3)$3x/x^2+2x-8=1/x-2+x/x+4$

after solving both side u will get

$3x=x+4+x-2$
3x=2x+2
x=2

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$1/x^2-1 =2/x^2+x-2$

1/(x-1)(x+1)=2/(x-1)(x+2)
u will get same will cross out each other
1/(x+1)=2/(x+2)
(x+2)=2(x+1)
x+2=2x+2
x=0