\fRationalizing the numerator or denominator This is common method used in calculation in calculus. The idea is to rationalize an expression using the fact that (VA - VB)(VA + VB) = A - B. Example Rationalize the denominator and numerator respectively in the following expressions: 9 th - 3 I 1 hSimplifying a compound fraction Sometimes algebraic expressions involve rational expressions in both the numerator and denominator. Example Simplify the following fractions: ath a 1 h -2Algebra of Rational Expressions We can simplify rational expressions by canceling factors with this rule AC A BC B Example Simplify the rational expression: 1:2- 9 - 4.r + 3We can multiply rational expressions according to the rule A C AC B D BD Example Multiply and simplify the following rational expressions 27 + 1 - 9 T- 3 5x + 4To divide rational expressions, we use the following rule: C A D B B C Example Divide and simplify the following rational expressions - 3 12 - 9 4 - 7x + 12To add rational expressions we use the rules B A+B C A B AD + BC C D CD In the latter case, we can simplify the calculation by using the Least Common Multiple of C and D. Example Add the following rational expressions and simplify the resulting rational expression 3 3 B 9 2