Algebra/Trig Review - Pauls Online Math Notes - Lamar University

Algebra/Trig Review6.SolutionIn this case don’t forget to always factor out any common factors first before goingany further.5 4 3 3 2 34x −8x − 32x = 4x x −2x− 8 = 4x x− 4 x+23125x − 8( ) ( )( )SolutionRemember the basic formulas for factoring a sum or difference of cubes.3 3 2 2a − b = a− b a + ab+bIn this case we’ve got( )( )( )( )a + b = a + b a − ab + b3 3 2 2( )( )3 2125 8 5 2 25 10 4x − = x− x + x+Simplifying Rational ExpressionsSimplify each of the following rational expressions.1.x22x−82− 4x+4SolutionThere isn’t a lot to these problems. Just factor the numerator and denominator asmuch as possible then cancel all like terms. Recall that you can only cancel termsthat multiply the whole numerator and whole denominator. In other words, you can’t2just cancel the x and you can’t cancel a 4 from the 8 in the numerator and the 4 inthe denominator. Things just don’t work this way.If you need convincing of this consider the following number example.17 8 + 9 4 + 98.5 = = ≠ = 132 2 1Here is the answer to this problem.222x−82( x − 4) 2( x− 2)( x+ 2)2( x+2)= = =2 22x − 4x+ 4 x − 4x+ 4 x − 2 x−2( )2.2x −5x−626x−xSolution© 2006 Paul Dawkins 19http://tutorial.math.lamar.edu/terms.aspx