x + 1 / x = 3/2
x + 1(2) = 3x
2x + 2 = 3x
-2x -2x
2/1 = 1x/1
2 = x
Is this correct?
If you are solving (x+1)/x = 3/2 and not x + (1/x) = 3/2, then your answer is correct.
Please use parentheses for clarification when what you type is ambiguous.
Thanks!
To solve the equation x + 1/x = 3/2, we can follow these steps:
Step 1: Get rid of the fraction
Multiply both sides of the equation by 2 to eliminate the denominator:
2(x + 1/x) = 2(3/2)
2x + 2/x = 3
Step 2: Remove the fraction in the equation
Multiply both sides of the equation by x to eliminate the fraction in the equation:
2x(x) + 2 = 3(x)
2x^2 + 2 = 3x
Step 3: Rearrange the equation to form a quadratic equation
Move all terms to one side of the equation to form a quadratic equation:
2x^2 - 3x + 2 = 0
Step 4: Solve the quadratic equation
The quadratic equation can be solved using factoring, completing the square, or the quadratic formula. In this case, we will factor the equation:
(2x - 1)(x - 2) = 0
Setting each factor equal to zero gives us two possible solutions:
2x - 1 = 0 or x - 2 = 0
Solving for x in each equation:
2x = 1 or x = 2
x = 1/2 or x = 2
So the possible solutions to the equation x + 1/x = 3/2 are x = 1/2 and x = 2.
Looking at your solution, it seems you made a mistake in Step 2 when you multiplied both sides by x. The correct equation should be 2x^2 + 2 = 3x. From there, you can solve it correctly to find the solutions x = 1/2 and x = 2.