HexMathv1.0.3

Simplify an expression

Type or scan an algebraic expression. HexMath simplifies it and shows every step.

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What this page covers

  • Combining like terms and distributing brackets, including a minus sign in front of a bracket.
  • Reducing an algebraic fraction by factoring the top and bottom, with the values that must be excluded.
  • Powers with the same base and simple radicals inside an expression.
  • Not covered here: solving an equation (use Solve an equation for x) and factoring as the goal (use Factor an expression).

How to enter the problem

  • Type or paste it. Use the math keyboard for fractions and powers, or type x^2 and / and it renders.
  • Scan it. Point the camera at the one expression and fit it in the frame.
  • Choose a photo. If the photo has several problems, they are solved as a list.
  • Write the instruction too if it helps, for example "Simplify". Then tap Solve.

Worked example

Problem

Simplify x2−9x2+x−6\displaystyle \dfrac{x^2 - 9}{x^2 + x - 6}.

Answer

Verified

The answer is

x−3x−2\dfrac{x - 3}{x - 2}, for x≠2x \neq 2 and x≠−3x \neq -3

Explanation

  1. Factor the numerator
    x2−9x^2 - 9 is a difference of squares: (x−3)(x+3)(x - 3)(x + 3).
  2. Factor the denominator
    x2+x−6=(x+3)(x−2)x^2 + x - 6 = (x + 3)(x - 2), since 3 and −2-2 multiply to −6-6 and add to 1.
  3. Note the excluded values
    The denominator is zero at x=−3x = -3 and x=2x = 2, so the expression is undefined there.
  4. Cancel the common factor
    (x+3)(x + 3) appears top and bottom and can be removed, because it is a factor, not a term.
  5. Write the result with its restriction

Common mistakes

  • Cancelling terms instead of factors, for example crossing out the x2x^2 on top and bottom. Only a factor of the whole numerator and the whole denominator can be cancelled.
  • Dropping the excluded value that belonged to the cancelled factor. x=−3x = -3 still makes the original expression undefined.
  • Losing the sign when distributing a minus over a bracket: −3(x−5)-3(x - 5) is −3x+15-3x + 15, not −3x−15-3x - 15.
  • Combining unlike terms, such as adding 2x2x and 3.

Checks, assumptions and limits

  • Check by substitution. Pick a value that is not excluded, say x=5x = 5. The original gives 16/24=2/316/24 = 2/3; the simplified form gives 2/32/3. If the two differ, a step is wrong.
  • The variable is treated as a real number. Domain restrictions come from denominators and even roots and must be carried into the answer.
  • "Simplest form" is a convention. A factored fraction with restrictions is the usual target here; a teacher may want a different form, so compare with the instruction you were given.
  • HexMath can make mistakes. Double check important steps.

Related tasks

Frequently asked questions

Yes. Use the camera and fit one expression in the frame, or choose a photo. A photo with several problems is solved as a list.

Both. The solution is a list of numbered steps, each with a short title, ending in a boxed final answer. You can ask a follow-up about any step.

No. You can try 1 math question today without signing in. Sign in for 3 a day.

You can type one and it will be reduced, but this page is written for algebraic expressions. Numeric fractions are ordinary arithmetic and need no page of their own.

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Last updated: · HexMath