A38 APPENDIX Review If a b and c b are two rational expressions, then + = + − = − ≠ a b c b a c b a b c b a c b b if 0 (4) Adding and Subtracting Rational Expressions with Unequal Denominators Perform the indicated operation and simplify the result. Leave your answer in factored form. (a) − + + − ≠ − x x x x x 3 4 2 4, 2 (b) − − ≠ − x x x x 4 1 2, 0, 2 2 2 Solution EXAMPLE 5 (a) x x x x x x x x x x x x x x x x x x x x x x x x x x x x 3 4 2 3 4 2 2 4 4 2 3 2 4 4 2 5 6 4 4 2 2 6 4 2 2 2 2 ( )( ) ( )( ) ( )( ) ( )( ) ( )( ) − + + − = − + ⋅ − − + + + ⋅ − = − − + + + − = − + + + + − = − + + − If a b and c d are two rational expressions, then + = ⋅ ⋅ + ⋅ ⋅ = + ≠ ≠ a b c d a d b d b c b d ad bc bd b d if 0, 0 (5a) − = ⋅ ⋅ − ⋅ ⋅ = − ≠ ≠ a b c d a d b d b c b d ad bc bd b d if 0, 0 (5b) Adding and Subtracting Rational Expressions with Equal Denominators Perform the indicated operation and simplify the result. Leave your answer in factored form. (a) − + + + + ≠ − x x x x x 2 4 2 5 3 2 5 5 2 2 (b) − − + − ≠ x x x x x 3 3 2 3 3 Solution EXAMPLE 4 (a) ( ) ( ) ( )( ) − + + + + = − + + + = + − + = − + + x x x x x x x x x x x x x 2 4 2 5 3 2 5 2 4 3 2 5 2 1 2 5 2 1 1 2 5 2 2 2 (b) ( ) ( ) − − + − = − + − = − − − = − − − = − + − x x x x x x x x x x x x x x 3 3 2 3 3 2 3 3 2 3 2 2 3 2 1 3 Now Work problem 23 If the denominators of two rational expressions to be added or subtracted are not equal, we can use the general formulas for adding and subtracting rational expressions. ( ) 5a æ
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