Solve 1/x + 1/3 = 2/3
Rational equation, worked out line by line the way a teacher would write it.
Answer
| Solution | x = 3 |
Step-by-step solution
8 steps-
1 Given\frac{1}{x} + \frac{1}{3} = \frac{2}{3}
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 3x
Multiplying every term on both sides by the least common denominator 3x cancels every fraction at once. The equation stays balanced because all terms were multiplied by the same thing.
3 x \left(\frac{1}{3} + \frac{1}{x}\right) = 3 x \frac{2}{3}This clears all the fractions.
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4 Cancel and simplifyx + 3 = 2 x
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5 Subtract 2x 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.
3 - x = 0Collect every term containing x on the left.
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6 Subtract 3 from both sides- x = -3
Move the constant terms to the right.
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7 Multiply both sides by −1
Multiplying both sides by −1 flips every sign. The equation stays true, and a positive variable or leading term is easier to read and to factor.
x = 3 -
8 Check\begin{aligned}x = 3:\quad \frac{2}{3} = \frac{2}{3}\quad\checkmark\end{aligned}
Substituting each solution back makes both sides equal.
Check by substitution
| x | Left side | Right side | |
|---|---|---|---|
| 3 | 2/3 | 2/3 | ✓ |
Change a number or try your own problem: the solver works it out the same way, with a graph and hint mode.