SOLUTION: Solve 1/x + 1/x+5 = 3/4

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Question 176562: Solve 1/x + 1/x+5 = 3/4
Found 2 solutions by MathTherapy, ankor@dixie-net.com:
Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

(1)(4)(x + 5) + (1)(4x) = (3)(x)(x + 5)
4x + 20 + 4x = 3x^2 + 15x
20 = 3x^2 + 15x - 8x
3x^2 + 7x - 20 = 0
(3x - 5)(x + 4) = 0
x = 5/3 or - 4

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Solve 1%2Fx + 1%2F%28x%2B5%29 = 3%2F4
mult eq by common denominator, 4x(x+5)
4x(x+5)*1%2Fx + 4x(x+5)*1%2F%28x%2B5%29 = 4x(x+5)*3%2F4
cancel out the denominators
4(x+5) + 4x = 3x(x+5)
;
4x + 20 + 4x = 3x^2 + 15x
:
8x + 20 = 3x^2 + 15x
;
0 = 3x^2 + 15x - 8x - 20
;
3x^2 + 7x - 20 = 0; a quadratic eq
factor this to
(3x - 5)(x + 4) = 0
two solutions
3x = 5
;
x = 5%2F3
and
x = -4
:
check both solutions in original eq