Rational equation workbench

Find x, then prove it belongs.

Equivalent algebra is only half the job. Track the excluded value, test a candidate, and leave with a proof you can inspect.

Start with the equation

x7 - 6x= 1

Before transforming anything, record where the denominator is zero.

  1. Restrict
  2. Multiply
  3. Collect
  4. Verify
1 of 4

Visual evidence

One intersection. One forbidden line.

Left sidey = 1Excluded
Left side1.000
Right side1.000
Residual0.000

Durable output

Your proof ledger

Saved locally

Restrictionx ≠ 7/6

Transformx = 7 - 6x

Collect7x = 7

Candidatex = 1

ConclusionVerify the candidate to finish.

Next: check x = 1 against the original denominator.

A denominator restriction, a candidate and the original-equation check

Read the explanation

For the source equation x divided by seven minus six x equals one, the denominator vanishes at seven sixths. A number line uses three hundred pixels per x unit: x equals one is at five hundred pixels and seven sixths is at five hundred fifty. Their separation is fifty pixels, representing one sixth. The valid candidate and the forbidden value are different points. The source numerical tester treats denominator magnitudes below ten to the minus eight as undefined; that is a numerical tolerance, not a change to the exact mathematical domain. Inside the allowed domain, multiplying by the nonzero denominator gives x equals seven minus six x. Adding six x to both sides gives seven x equals seven, then x equals one. At forty pixels per unit, the bars show one x plus six x, a total seven x units. The resulting candidate is not accepted until the original expression is checked. At x equals one, seven minus six equals one, the quotient is one and its residual against one is zero. The bars compare denominator seven at x equals zero with denominator one at x equals one, using forty pixels per unit. Zero divided by seven equals zero, so its residual from one is minus one. One divided by one equals one, with residual zero. The local tester supports integer fractions, stores step and candidate text, but reload does not restore the verdict. Copy and download preserve the source proof template; an invalid-input warning also uses its denominator-zero wording in that template. This is one fixed educational equation, not a general symbolic proof engine.

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