Cancelling out is a mathematical process used for removing subexpressions from a mathematical expression, when this removal does not change the meaning or the value of the expression because the subexpressions have equal and opposing effects.
[1] For example, a fraction is put in lowest terms by cancelling out the common factors of the numerator and the denominator.
At times, cancelling out can introduce limited changes or extra solutions to an equation.
But cancelling 'naively' like this, will mean we don't get all the solutions (sets of (a, b) satisfying the inequality).
In computational science, cancelling out is often used for improving the accuracy and the execution time of numerical algorithms.