SOLUTION: 1/x + 1/(x+1) = 15/56

Question 407624: 1/x + 1/(x+1) = 15/56
Answer by graphmatics(170) (Show Source): You can put this solution on YOUR website!
1/x + 1/(x+1) = 15/56
multiply both sides by (x)*(x+1) and get
1/x*(x*(x+1)) + (1/(x+1))*(x*(x+1)) = (15/56)*(x*(x+1))
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(x+1) + x = (15/56)*(x^2 + x)
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2*x + 1 = (15/56)*x^2 +(15/56)*x
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-0.2678*x^2 -0.2678*x +2*x +1 = 0
-0.2678*x^2 + 1.7321*x + 1 = 0

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=4.07137041 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: -0.533352716778202, 7.00123919922779. Here's your graph:

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