SOLUTION: Hi, Please help me with this problem... (1/x+8)+(1/x+5) = 1/2 Thank you in advance for your time and assistance...

Algebra ->  Rational-functions -> SOLUTION: Hi, Please help me with this problem... (1/x+8)+(1/x+5) = 1/2 Thank you in advance for your time and assistance...       Log On


   

Question 685591: Hi,
Please help me with this problem...
(1/x+8)+(1/x+5) = 1/2
Thank you in advance for your time and assistance...

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Hi,
Please help me with this problem...
(1/x+8)+(1/x+5) = 1/2
Thank you in advance for your time and assistance...

I'm assuming it's 1%2F%28x+%2B+8%29+%2B+1%2F%28x+%2B+5%29+=+1%2F2, as opposed to %281%2Fx%29+%2B+8+%2B+%281%2Fx%29+%2B+5+=+1%2F2

Note that x+%3C%3E+-+8, or x+%3C%3E+-+5

Solving the former:
2(x + 5) + 2(x + 8) = (x + 8)(x + 5) ------- Multiplying by LCD, 2(x + 8)(x + 5)

2x+%2B+10+%2B+2x+%2B+16+=+x%5E2+%2B+13x+%2B+40

4x+%2B+26+=+x%5E2+%2B+13x+%2B+40

x%5E2+%2B+13x+-+4x+%2B+40+-+26+=+0

x%5E2+%2B+9x+%2B+14+=+0

(x + 7)(x + 2) = 0

highlight_green%28x+=+-+7%29 OR highlight_green%28x+=+-+2%29

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