SOLUTION: (10/x) +3= (x+9)/(x-4) solve using LCD Check for extraneous solution

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Question 729767: (10/x) +3= (x+9)/(x-4)
solve using LCD
Check for extraneous solution
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
(10/x) +3= (x+9)/(x-4)
solve using LCD
Check for extraneous solution
***
(10/x) +3= (x+9)/(x-4)
LCD:x(x-4)
10x-40+3x(x-4)=x(x+9)
10x-40+3x^2-12x=x^2+9x
2x^2-11x-40=0
(2x+5)(x-8)=0
x=-5/2
or
x=8
check:
for x=8
10/8+3=(8+9)/(8-4)
34/8=17/4
17/4=17/4
left side=right side
...
for x=-5/2
10/(-5/2)+3=((-5/2)+9)/((-5/2)-4)
(20/-5)+3=((-5/2)+(18/2))/((-5/2)-(8/2))
(-4+3)=(13/2)/(-13/2)
-1=-1
left side=right side
No extraneous solutions