Solve for x x+1/x=2

Problem

x+1/x=2

Solution

1. Multiply the entire equation by x to eliminate the fraction, assuming x≠0

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

2. Distribute x on the left side of the equation.

x2+1=2*x

3. Rearrange the equation into standard quadratic form a*x2+b*x+c=0 by subtracting 2*x from both sides.

x2−2*x+1=0

4. Factor the quadratic expression, recognizing it as a perfect square trinomial.

(x−1)2=0

5. Solve for x by taking the square root of both sides.

x−1=0

x=1

Final Answer

x=1

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