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Rational equationsAlgebraHigh schoolabout 1:08

Solve 1/x + 1/(2x) = 3: animated lesson

A narrated, step-by-step rational equations video lesson with captions. Final answer: x = 1/2 ≈ 0.5.

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Transcript

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. The problem
Solving an equation
$\frac{1}{ x}+\frac{1}{2~ x} = 3$
2. Steps, part 1
1. $\frac{1}{ x}+\frac{1}{2~ x} = 3$
  Start with the equation
2. $-6x^{2} + 3x = 0$
  Multiply both sides by $2\cdot{ x}^{2}$ to clear the fractions
3. $-6x^{2} + 3x = 0$
  Move every term to one side to get standard form
4. $\Delta = b^2 - 4ac = 3^2 - 4 \cdot (-6) \cdot 0 = 9$
  Compute the discriminant
3. Steps, part 2
1. Δ > 0, so there are two distinct real roots
2. $x = \frac{-b \pm \sqrt{\Delta}}{2a} = \frac{-3 \pm \sqrt{9}}{-12} = \frac{-3 \pm 3}{-12}$
  Apply the quadratic formula
3. $x_1 = \frac{-3 - 3}{-12} = \frac{1}{2},\quad x_2 = \frac{-3 + 3}{-12} = 0$
  Simplify each root
4. $-6x^2 + 3x = -3x(2x - 1)$
  Factored form
4. Steps, part 3
1. Remove extraneous roots
5. The answer
$x = \frac{1}{2} \approx 0.5$
Δ = 9; x = 1/2 ≈ 0.5
6. Check
- x = 0.5: left side = 3, right side = 3 ✓

Transcript

The problem. Here is the problem: 1/x plus 1/(2x) equals 3. A quadratic equation in x: solve with the quadratic formula.

Steps, part 1. Start with the equation. Multiply both sides by 2 cdot x ^ 2 to clear the fractions. This is only valid where 2 times x ^ 2 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 greater than 0, so there are two distinct real roots. Apply the quadratic formula. Simplify each root. Factored form.

Steps, part 3. Remove extraneous roots. x equals 0 makes a denominator zero and is rejected.

The answer. So the answer is x equals 1 over 2 approximately 0.5. The quadratic formula gives every solution of ax squared plus bx plus c equals 0.

Check. x equals 0.5: 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 1/x + 1/(2x) = 3: Animated Step-by-Step Lesson