Algebraic fractions
Type two algebraic fractions — x/3 + 1/6, x/4 + x/6, 2x/5 + x/3 — and the calculator finds the least common denominator, rewrites each term, combines like terms, and simplifies, naming every rule it uses.
Algebra addition tool
Type two terms with the same variable — the tool finds the common denominator and combines the numerators step by step.
Examples: x/3 + 1/6, x/4 + x/6, 2x/5 + x/3, or 1/2 + x/8.
Derivation
x/4 + x/6
= 3x/12 + 2x/12
= 5x/12
What it computes
Worked example
x/4 + x/6 = 3x/12 + 2x/12 = 5x/12
The least common denominator of 4 and 6 is 12. Both numerators carry an x, so after the rewrite they merge: 3x + 2x = 5x. The variable never touched the denominator work.
Worked example
2x/5 + x/3 = 6x/15 + 5x/15 = 11x/15
Stretching 2x/5 to fifteenths multiplies the whole numerator by 3 — 6x, not 2x. The full numerator feels the same stretch the denominator does.
Worked example
x/3 + 1/6 = 2x/6 + 1/6 = (2x + 1)/6
One numerator has an x and the other does not, so 2x and 1 cannot merge. The single bar over 2x + 1 is the finished answer — no further simplification exists.
Worked example
x/3 + x/6 = 2x/6 + x/6 = 3x/6 = x/2
The combined numerator 3x and denominator 6 share the factor 3, so the sum reduces to x/2. Simplify variable fractions exactly as numeric ones — divide top and bottom by the shared factor.
For x/4 + x/6, the calculator finds the least common denominator of 4 and 6 — twelve — and rewrites each term in that unit: 3x/12 and 2x/12. The numerators are like terms (both count x’s), so they merge to 5x, and the answer 5x/12 is checked for reduction before it is shown. Nothing about the variable changed the denominator work; twelfths are twelfths whether or not an x rides on top.
For deeper work — subtracting variable fractions, simplifying products like 2x/3 × 6/x², or solving equations whose variable sits under the bar — the guides below walk the same rules by hand, and the tools on those pages verify each result.
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Common questions
