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Rational equationsAlgebraHigh schoolabout 0:55

Solve x/(x-2) = 3: animated lesson

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

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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
$\frac{ x}{ x-2} = 3$
2. Step by step
1. $\frac{ x}{ x-2} = 3$
  Start with the equation
2. $-2x + 6 = 0$
  Multiply both sides by $x-2$ to clear the fractions
3. $x = \frac{-6}{-2} = 3$
  Isolate x
3. On the graph
Each solution is where the graph of left side minus right side crosses zero.
4. The answer
$x = 3$
x = 3
5. Check
- x = 3: left side = 3, right side = 3 ✓

Transcript

The problem. Here is the problem: x/(x minus 2) equals 3. A linear equation in x: isolate x using inverse operations.

Step by step. Start with the equation. Multiply both sides by x minus 2 to clear the fractions. This is only valid where x minus 2 not equal to 0, so any value that makes it zero is excluded at the end. Isolate x.

On the graph. Now look at the graph of the left side minus the right side. It crosses zero exactly at the solutions we found.

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

Check. x equals 3: left side equals 3, right side equals 3, which checks out.

About rational equations

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

Solve x/(x-2) = 3: Rational equations Step-by-Step Lesson