# Math operation questions

DQ Rational expression is very much similar to fraction and therefore doing operations—adding, subtracting, multiplying, and dividing—with rationalexpressions is similar to doing operations with fractions. When we multiply rational expressions, we multiply numerators and multiply denominators. For dividing by a rational expression, we multiply by its reciprocal. For adding and subtracting rational expressions, we take least common multiple, (LCM) of denominators so as to have same denominator in every expressions and than we add (or subtract) the numerators. Both fractions and rational expressions follow the same rule for doing operations. Therefore, understanding how to work with one kind of problem can help understand how to work another type.
Truly speaking, I have no idea when I might use this skill in real life. However, I think I might use this skill when I have a proportion with unknown value in numerator or denominator or in both.
DQ 2
We find the greatest common factor of a polynomial by using Factorization Method. First, we factorize each polynomial and then take out the product of common factor from each polynomial. For example:
4×2– 25 and 4×2 + 20x + 25
4×2 – 25 = (2x + 5)(2x – 5)
4×2 + 4x + 1 = (2x + 5)2
Only common factor is (2x + 5), therefore, GCF of (4×2 – 25) and (4×2 + 20x + 25) is (2x + 5).
When finding the greatest common factor of a polynomial, it cannot be larger than the smallest coefficient. However, it can be smaller than the smallest coefficient (in case no common factor).