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Rational equationsAlgebraHigh schoolabout 0:55

Solve x/(x - 5) + 5/(x - 4) = 1: animated lesson

A narrated, step-by-step rational equations video lesson with captions. Final answer: x = 9/2 ≈ 4.5.

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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
$\frac{ x}{ x-5}+\frac{5}{ x-4} = 1$
2. Step by step
1. $\frac{ x}{ x-5}+\frac{5}{ x-4} = 1$
  Start with the equation
2. $10x - 45 = 0$
  Multiply both sides by ${ x}^{2}-9\cdot x+20$ to clear the fractions
3. $x = \frac{45}{10} = \frac{9}{2}$
  Isolate x
3. The answer
$x = \frac{9}{2} \approx 4.5$
x = 9/2 ≈ 4.5
4. Check
- x = 4.5: left side = 1, right side = 1 ✓

Transcript

The problem. Here is the problem: x/(x minus 5) plus 5/(x minus 4) equals 1. A linear equation in x: isolate x using inverse operations.

Step by step. Start with the equation. Multiply both sides by x ^ 2 -9 cdot x plus 20 to clear the fractions. This is only valid where x ^ 2 minus 9 times x plus 20 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 9 over 2 approximately 4.5. Doing the same operation to both sides keeps the equation balanced. Undoing addition, then multiplication, leaves x alone.

Check. x equals 4.5: left side equals 1, right side equals 1, which checks out.

About rational equations

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

Solve x/(x - 5) + 5/(x - 4) = 1: Rational equations Lesson