Skip to content
MathSolver Pro
  • Open the math solver
  • Ask the AI tutor
  • Find an AP course
  • Create a quiz
  • Open the calculator
  • Graphing Calculator
  • Browse all calculators
  • Read math guides
↑ ↓Enter to open · Esc to close
Solve a problem
Rational equationsAlgebraHigh schoolabout 1:02

Solve 4/(x^2-4) = 1/(x-2): animated lesson

A narrated, step-by-step rational equations video lesson with captions. Final answer: No solution.

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
    Solving an equation
    4x2−4=1x−2\frac{4}{{ x}^{2}-4} = \frac{1}{ x-2}
  2. 2. Steps, part 1
    1. 4x2−4=1x−2\frac{4}{{ x}^{2}-4} = \frac{1}{ x-2}
      Start with the equation
    2. −x2+4x−4=0-x^{2} + 4x - 4 = 0
      Multiply both sides by x3−2⋅x2−4⋅x+8{ x}^{3}-2\cdot{ x}^{2}-4\cdot x+8 to clear the fractions
    3. −x2+4x−4=0-x^{2} + 4x - 4 = 0
      Move every term to one side to get standard form
    4. Δ=b2−4ac=42−4⋅(−1)⋅(−4)=0\Delta = b^2 - 4ac = 4^2 - 4 \cdot (-1) \cdot (-4) = 0
      Compute the discriminant
  3. 3. Steps, part 2
    1. Δ = 0, so there is one repeated real root
    2. x=−b2a=−4−2=2x = \frac{-b}{2a} = \frac{-4}{-2} = 2
      Apply the quadratic formula
    3. −x2+4x−4=−(x−2)2-x^2 + 4x - 4 = -(x - 2)^2
      Factored form
    4. Remove extraneous roots
  4. 4. The answer
    No solution\text{No solution}

    Δ = 0; No solution

Transcript

The problem. Here is the problem: 4/(x squared minus 4) equals 1/(x minus 2). A quadratic equation in x: solve with the quadratic formula.

Steps, part 1. Start with the equation. Multiply both sides by x ^ 3 -2 cdot x ^ 2 -4 cdot x plus 8 to clear the fractions. This is only valid where x ^ 3 minus 2 times x ^ 2 minus 4 times x plus 8 not equal to 0, so any value that makes it zero is excluded at the end. Move every term to one side to get standard form. Compute the discriminant.

Steps, part 2. delta equals 0, so there is one repeated real root. Apply the quadratic formula. Factored form. Remove extraneous roots. x equals 2 makes a denominator zero and is rejected.

The answer. So the answer is No solution. The quadratic formula gives every solution of ax squared plus bx plus c equals 0.

About rational equations

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

More lessons like this

Solve 4/(x^2-4) = 1/(x-2): Animated Step-by-Step Lesson