Question 109156: This problem is not in the book.
15/x - 15/x+2 =2 Can you help me solve this? Thanks Rhee Found 2 solutions by edjones, ankor@dixie-net.com:Answer by edjones(8007) (Show Source):
You can put this solution on YOUR website! (15/x)-(15/(x+2))=2
15(x+2)-15x=2x(x+2) multiply both sides times x(x+2) to eliminate fractions.
15x+30-15x=2x^2+4x
2x^2+4x-30=0 add -30 to both sides.
2(x^2+2x-15)=0
(x+5)(x-3)=0 factor
x=-5, x=3
Always check:
15/-5 - 15/-3=2...-3+5=2 true
15/3 - 15/5=2...5-3=2 true
Ed
You can put this solution on YOUR website! 15/x - 15/x+2 = 2
; - = 2
:
The common denominator will be x(x+2)
Multiply equation by that:
x(x+2)* - x(x+2)* = x(x+2) * 2
:
Cancel out the denominators and you have:
15(x+2) - 15x = 2x(x+2)
:
15x + 30 - 15x = 2x^2 + 4x
:
The 15x's cancel; subtract 30 from both sides, you have a quadratic equation
2x^2 + 4x - 30 = 0
:
Factor this to:
(2x - 6)(x + 5) = 0
:
Two solutions:
2x = +6
x = 6/2
x = 3
and
x = - 5
:
Check both solutions in the original equation:
x = 3 - = 2
5 - 3 = 2; a good solution
: - = 2
-3 - (-5) = 2; also a good solution
:
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