Rational Expressions and Adding Them

Rational Expressions and Adding Them

Rational expressions involve fractions with variables in both the numerator and denominator. They can be added together if they have similar denominators. To do this, you combine like terms under the common factor and simplify the resultant fraction. For instance, consider ( \frac{x}{y} + \frac{z^2}{y} ) where y is any nonzero expression. By combining the two fractions we get [ \frac{x+z^2}{y} = \boxed{\frac{(x+z^2)}{y}} ] This means that when adding these types of fractions, you just replace them by the sum of their numerators divided by the common denominator. It's important to note though that if one term has an algebraic expression as its denominator while another has a constant as its denominator, there will be no common denominator and therefore they cannot be combined in this manner. Instead, you must convert them into equivalent fractions before adding them up. Overall, when dealing with rational expressions, it helps to rewrite each fraction so it shares a common factor between all the terms within it, allowing for easier combination.