Solve (x + 5)/(x − 2) = 2
Rational equation, worked out line by line the way a teacher would write it.
Answer
| Solution | x = 9 |
Step-by-step solution
8 steps-
1 Given\frac{x + 5}{x - 2} = 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 2 -
3 Multiply every term by the least common denominator x - 2
Multiplying every term on both sides by the least common denominator x - 2 cancels every fraction at once. The equation stays balanced because all terms were multiplied by the same thing.
\frac{x + 5}{x - 2} \left(x - 2\right) = \left(x - 2\right) 2This clears all the fractions.
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4 Cancel and simplifyx + 5 = 2 x - 4
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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.
5 - x = -4Collect every term containing x on the left.
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6 Subtract 5 from both sides- x = -9
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 = 9 -
8 Check\begin{aligned}x = 9:\quad 2 = 2\quad\checkmark\end{aligned}
Substituting each solution back makes both sides equal.
Check by substitution
| x | Left side | Right side | |
|---|---|---|---|
| 9 | 2 | 2 | ✓ |
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