Solve (x + 2)/(x − 1) = 4
Rational equation, worked out line by line the way a teacher would write it.
Answer
| Solution | x = 2 |
Step-by-step solution
9 steps-
1 Given\frac{x + 2}{x - 1} = 4
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 1 -
3 Multiply every term by the least common denominator x - 1
Multiplying every term on both sides by the least common denominator x - 1 cancels every fraction at once. The equation stays balanced because all terms were multiplied by the same thing.
\frac{x + 2}{x - 1} \left(x - 1\right) = \left(x - 1\right) 4This clears all the fractions.
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4 Cancel and simplifyx + 2 = 4 x - 4
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5 Subtract 4x 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 - 3 x = -4Collect every term containing x on the left.
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6 Subtract 2 from both sides- 3 x = -6
Move the constant terms to the right.
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7 Divide both sides by -3
Dividing both sides by -3 undoes the multiplication by -3, so the variable is left on its own. Both sides change in the same way, so the equation stays true (dividing by 0 is the one thing that is never allowed).
x = \frac{-6}{-3} -
8 Simplifyx = 2
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9 Check\begin{aligned}x = 2:\quad 4 = 4\quad\checkmark\end{aligned}
Substituting each solution back makes both sides equal.
Check by substitution
| x | Left side | Right side | |
|---|---|---|---|
| 2 | 4 | 4 | ✓ |
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