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Rational equationsAlgebraHigh schoolabout 0:49

Solve 1/(x-1) = 2: animated lesson

A narrated, step-by-step rational equations video lesson with captions. Final answer: x = 3/2 ≈ 1.5.

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Video with a synthetic English voice and captions. Pick another language for subtitles in that language, or open the interactive version.

Video narrated by a synthetic voice (Piper TTS, en_US-ljspeech-high voice (LJ Speech dataset, public domain)); the steps come from our maths engine and the answer was checked independently. Download MP4 (0.3 MB) · Captions (WebVTT)

Steps on screen

1. The problem
Solving an equation
$\frac{1}{ x-1} = 2$
2. Step by step
1. $\frac{1}{ x-1} = 2$
  Start with the equation
2. $-2x + 3 = 0$
  Multiply both sides by $x-1$ to clear the fractions
3. $x = \frac{-3}{-2} = \frac{3}{2}$
  Isolate x
3. The answer
$x = \frac{3}{2} \approx 1.5$
x = 3/2 ≈ 1.5
4. Check
- x = 1.5: left side = 2, right side = 2 ✓

Transcript

The problem. Here is the problem: 1/(x minus 1) equals 2. A linear equation in x: isolate x using inverse operations.

Step by step. Start with the equation. Multiply both sides by x minus 1 to clear the fractions. This is only valid where x minus 1 not equal to 0, so any value that makes it zero is excluded at the end. Isolate x.

The answer. So the answer is x equals 3 over 2 approximately 1.5. Doing the same operation to both sides keeps the equation balanced. Undoing addition, then multiplication, leaves x alone.

Check. x equals 1.5: left side equals 2, right side equals 2, which checks out.

About rational equations

Solve equations with variables in the denominator and reject values that make a denominator zero.

Solve 1/(x-1) = 2: Rational equations Step-by-Step Lesson