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Simplifying expressionsAlgebraHigh schoolabout 0:52

Simplify (x^4 - 1)/(x^2 + 1): animated lesson

A narrated, step-by-step simplifying expressions video lesson with captions. Final answer: (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 (0.3 MB) · Captions (WebVTT)

Steps on screen

  1. 1. The problem
    Worked example
    x4−1x2+1\frac{{x}^{4}-1}{{x}^{2}+1}
  2. 2. Step by step
    1. x4−1x2+1\frac{x^{4} - 1}{x^{2} + 1}
      Write as a single fraction
    2. (x−1)(x+1)(x2+1)x2+1\frac{(x - 1)(x + 1)(x^{2} + 1)}{x^{2} + 1}
      Factor the numerator and denominator
    3. (x−1)(x+1)1\frac{(x - 1)(x + 1)}{1}
      Cancel the common factor
    4. State the excluded values
  3. 3. The answer
    (x−1)(x+1)(x - 1)(x + 1)

    (x^4 - 1)/(x^2 + 1) = (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: (x to the power 4 minus 1)/(x squared 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. Cancel the common factor. The factor x squared plus 1 appears in both the numerator and the denominator. Cancelling it does not change the value wherever the original expression is defined. State the excluded values. No real value makes a denominator zero.

The answer. So the answer is (x minus 1)(x plus 1). In lowest terms the result is (x minus 1)(x plus 1) (expanded: x squared minus 1). Excluded values: none.

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.

More lessons like this

Simplify (x^4 - 1)/(x^2 + 1): Animated Step-by-Step Lesson