Solve for x 1/x+1/(x+2)=1/2

Problem

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

Solution

1. Find a common denominator for the terms on the left side of the equation, which is x*(x+2)

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

2. Combine the fractions on the left side by adding the numerators.

(2*x+2)/(x2+2*x)=1/2

3. Cross-multiply to eliminate the denominators.

2*(2*x+2)=1*(x2+2*x)

4. Distribute and rearrange the equation into a standard quadratic form a*x2+b*x+c=0

4*x+4=x2+2*x

x2−2*x−4=0

5. Apply the quadratic formula x=(−b±√(,b2−4*a*c))/(2*a) where a=1 b=−2 and c=−4

x=(−(−2)±√(,(−2)2−4*(1)*(−4)))/(2*(1))

x=(2±√(,4+16))/2

6. Simplify the radical and the resulting expression.

x=(2±√(,20))/2

x=(2±2√(,5))/2

x=1±√(,5)

Final Answer

1/x+1/(x+2)=1/2⇒x=1±√(,5)

Want more problems? Check here!