SOLUTION: Have reason to believe an error somewhere in my following steps... Original problem: 1/x + 2/(x+2) = 17/35 Using LCD to clear fractions, I get: 35x + 70 + 70x = 17x^2 + 3

Question 860328: Have reason to believe an error somewhere in my following steps...
Original problem: 1/x + 2/(x+2) = 17/35
Using LCD to clear fractions, I get:
35x + 70 + 70x = 17x^2 + 34
Rewriting to standard quadratic form:
17x^2 -105x -36 = 0
Factoring by grouping I get:
17x^2 -18x +34x -36
(17x^2 +34x) +(-18x -36)
17x(x+2) -18(x+2)
(17x-18)(x+2)= 0
However, when I FOIL last expression above, I get:
17x^2 +16x -36 ???
Shouldn't FOIL result in expression I had above for standard quadratic form -- 17x^2 -105x -36 =0 ?
Thanks much

Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!

LCD = 35x(x+2)
35(x+2)+2*35*x = 17x(x+2)

35x+70+70x=17x^2+34x
17x^2-71x-70=0
solve for x
you will get x= 5 or -0.82
plug the values in the equation to check

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