Simplifying expressions

The app transforms an expression without an equals sign according to the chosen chip: it simplifies it (a rational expression over a common denominator and cancelled, with conditions), expands it, factors it (by taking out a common factor, by formulas and by synthetic division) or splits it into partial fractions – as on paper, with equations for the unknown coefficients. Factoring is over the integers; if the expression factors further over the reals (by irrational roots), the next step shows it. A root of a monomial is taken out partly – with an even root as an absolute value where the base may be negative. Complex numbers work too – a quotient by multiplying with the complex conjugate.

Examples

Simplifying a rational expression.
Input: (x^2 - 1)/(x^2 + 2x + 1) Simplify
(x^2 - 1)/(x^2 + 2x + 1)
Expanding.
Input: (x + 2)^3 Expand
(x + 2)^3
Factoring by synthetic division.
Input: x^3 - 6x^2 + 11x - 6 Factor
x^3 - 6x^2 + 11x - 6
Partial fractions.
Input: (3x + 5)/(x^2 + x - 2) Partial fractions
(3x + 5)/(x^2 + x - 2)
Taking a root out partly, with an absolute value.
Input: sqrt(8a^5 b^2) Simplify
sqrt(8a^5 b^2)
Dividing complex numbers.
Input: (3+4i)/(1-2i) Simplify
(3+4i)/(1-2i)