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

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Romel's picture
Solve for x: 1/x + 1/(x + 2) = 1

Determine the value of x from the following equation:
$\dfrac{1}{x} + \dfrac{1}{x + 2} = 1$

esmilitar's picture
X= the square root of 2

X= the square root of 2
Simplify the given equation
1/x + 1/(x+2)=1
=>(( x+2) + x )/(x (x+2)) =1
=>(2x+2)/x(x+2)=x(x+2)/x(x+2)
=>2x +2=x^2+2x
=>x^2+2x-2x=2
=>x^2=2
Thus X= the square root of 2 ans.
To verify the answer substitute the value of x=the square root 2 from the given equation if it satisfies equals to 1
Using the calculator by typing the equation using Alpha X and Shift solve it will gives you an answer x= 1.414213562 which is the value of square root of 2.