Solve 1/x + 1/2 = 1/2
Rational equation, worked out line by line the way a teacher would write it.
Answer
| Solution | no real solution |
Step-by-step solution
6 steps-
1 Given\frac{1}{x} + \frac{1}{2} = \frac{1}{2}
Solve for x.
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2 Note the values that make a denominator zero — they can never be solutions
Dividing by zero is undefined, so a value that makes a denominator 0 can never be a solution, even if it turns up as an answer later.
x \neq 0 -
3 Multiply every term by the least common denominator 2x
Multiplying every term on both sides by the least common denominator 2x cancels every fraction at once. The equation stays balanced because all terms were multiplied by the same thing.
2 x \left(\frac{1}{2} + \frac{1}{x}\right) = 2 x \frac{1}{2}This clears all the fractions.
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4 Cancel and simplifyx + 2 = x
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5 Subtract x from both sides
An equation stays true as long as you do the same thing to both sides, like adding the same weight to both pans of a balance. Adding or subtracting the same amount on both sides moves a term to the other side, where it appears with the opposite sign.
2 = 0Collect every term containing x on the left.
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6 The variable cancels and a false statement remains2 = 0
No value of x can make this true.
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