solving with fractions: 1/x + 1/(x+2) = 1/4

[almostbrain]

1/x + 1/(x+2) = 1/4

i know to multiply the numerater by denominator to get like denominators, but i have no idea how to solve the rest of the problem. Please HELP!!!!

This is where I am in the problem:

(2x+2)/(x^2 +2x) = (x^2 +2x)/4

 

[tkhunny]

"i know to multiply the numerater by denominator to get like denominators"

No. That part needs some work, too.

Who cares about "like denominators"? Get rid of the denominators.

1/x + 1/(x+2) = 1/4

Multiply by x

1 + x/(x+2) = x/4

Multiply by (x+2)

(x+2) + x = x*(x+2)/4

Multiply by 4

4(x+2) + 4x = x*(x+2)

Now what?

 

[arthur ohlsten]

1/x + 1/(x+2)= 1/4

multiply both sides by x[x+2]4 after simplifying we have
[x+2]4 + x4 = x[x+2] clear brackets
4x+8 +4x=x^2+2x combine likes on each side of = sign
8x+8=x^2+2x subtract 8x+8 from each side
0=x^2+2x-8x-8 combine likes
0=x^2-6x-8 can't be factored

 

[almostbrain]

thanks

thanks!! i was going by what the book said, and it obviously wasn't helpin any. once you get to that step though, you continue to solve using the quadratic formula. correct?

 

[tkhunny]

You got it, except for one thing. Since it started out in a different form, we need to review the ORIGINAL form for additional insight. In this case x ≤ 0. There are other restrictions. Can you find them?

You can cover these "Domain" problems by simply checking your answers in the ORIGINAL equation before you think you are done.