Question

when writing an equivalent rational expression, why do you multiply both the numerator and denonminator by the same factor?

Answer 1

When writing an equivalent rational expression, we multiply both the numerator and denominator by the same factor to ensure that the value of the expression does not change.

In mathematics, multiplying a number by 1 does not change its value. By multiplying both the numerator and denominator by the same factor (which is essentially multiplying by 1), we are not altering the value of the original expression.

However, by multiplying both the numerator and denominator by the same factor, we can manipulate the expression to a desired form. This can be helpful when simplifying the expression or when trying to write it in a different format.