Complex Fractions and Equations with Rational Expressions
- Page ID
- 221404
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Complex Fractions and Equations with Rational Expressions Complex Fractions First we begin with a complex fraction that contains no variables. Example 1 5 1 5
6 - 10 4
Notice we first multiplied by the total Least Common Denominator, then we simplified.
Complex Fractions Involving Expressions When we have a complex fraction with rational expressions as the numerator and denominator, we follow similar steps, except, of course factoring plays a key role.
Note: Usually you will not have to do all of the steps.
Example: 7 7
x + 1 - 7 x - 6
Cross Multiplication Recall that if then ad = bc The same hold true for functions: f g then fg = hk
Example Solve. 3x - 1 x + 2
Solution We cross multiply 9x2 + 12x - 3x - 4 = 5x2 + 10x - 2x - 4 9x2 + 9x - 4 = 5x2 + 8x - 4 4x2 + x = 0 x (4x + 1) = 0 1
Caution: Always check and see that the solution works by plugging back into the original equation!
Equations with Rational Expressions To solve equations that involve rational expressions, we following the following steps:
Example Solve 3 4 48 Solution First factor. 3 4 48 Then multiply by the LCD (x - 6)(x+ 6). 3 4 48
3(x + 6) - 4(x - 6) = 48 3x + 18 - 4x + 24 = 48 -x + 42 = 48 -x = 6 x = -6 Notice that -6 cannot be put back into the original equation, since there would be a zero in the denominator. We can conclude that this equation has no solution.
Back to the Absolute Values, Factoring and Arithmetic of Rational Expressions Page
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