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Simplifying expressionsAlgebraHigh schoolabout 0:58

Simplify (1/2)x + (1/3)x: animated lesson

A narrated, step-by-step simplifying expressions video lesson with captions. Final answer: (5/6)x.

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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
Worked example
$\frac{1}{2} x+\frac{1}{3} x$
2. Step by step
1. $\frac{1}{2} x+\frac{1}{3} x$
  Read the expression
2. Combine like terms
3. $\frac{5}{6}x$
  Write the result in standard form
3. The answer
$\frac{5}{6}x$
(1/2)x + (1/3)x = (5/6)x
4. Check
- Spot check at x = 0.73: original 0.6083333333, simplified 0.6083333333 ✓

Transcript

The problem. Here is the problem: (1 over 2)x plus (1 over 3)x. Simplify the polynomial expression in x.

Step by step. Read the expression. Combine like terms. x: 1 over 2 plus 1 over 3 equals 5 over 6. Like terms have identical variables and exponents, so only their coefficients are added. Write the result in standard form. Terms are ordered by descending total degree.

The answer. So the answer is (5 over 6)x. After expanding and combining like terms the expression is (5 over 6)x, a polynomial of degree 1 with 1 term.

Check. Spot check at x equals 0.73: original 0.6083333333, simplified 0.6083333333, which checks out.

About simplifying expressions

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

Simplify (1/2)x + (1/3)x: Animated Step-by-Step Lesson