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Simplifying expressionsAlgebraHigh schoolabout 1:10

Simplify 1/(x-1) - 1/(x+1): animated lesson

A narrated, step-by-step simplifying expressions video lesson with captions. Final answer: 2/((x - 1)(x + 1)), for x ≠ -1, x ≠ 1.

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 (0.4 MB) · Captions (WebVTT)

Steps on screen

  1. 1. The problem
    Worked example
    1x−1−1x+1\frac{1}{x-1}-\frac{1}{x+1}
  2. 2. Step by step
    1. 2x2−1\frac{2}{x^{2} - 1}
      Write as a single fraction
    2. 2(x−1)(x+1)\frac{2}{(x - 1)(x + 1)}
      Factor the numerator and denominator
    3. No common factors remain
    4. State the excluded values
  3. 3. The answer
    2(x−1)(x+1)\frac{2}{(x - 1)(x + 1)}

    1/(x-1) - 1/(x+1) = 2/((x - 1)(x + 1))

  4. 4. Check
    • The simplified form was compared with the original at four test points and agrees.

Transcript

The problem. Here is the problem: 1/(x minus 1) minus 1/(x plus 1). Simplify the rational expression in x: factor, cancel common factors and state excluded values.

Step by step. Write as a single fraction. Factor the numerator and denominator. No common factors remain. The numerator and denominator share no polynomial factor, so the fraction is already in lowest terms. State the excluded values. The original expression is undefined where any denominator (or divisor) is zero: x not equal to negative 1, x not equal to 1. These restrictions stay even if a factor cancelled.

The answer. So the answer is 2/((x minus 1)(x plus 1)), for x not equal to negative 1, x not equal to 1. In lowest terms the result is 2/((x minus 1)(x plus 1)) (expanded: 2/(x squared minus 1)). Excluded values: x not equal to negative 1, x not equal to 1.

Check. The simplified form was compared with the original at four test points and agrees.

About simplifying expressions

Simplify algebraic and rational expressions by collecting like terms and cancelling common factors.

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Simplify 1/(x-1) - 1/(x+1): Animated Step-by-Step Lesson