Math 017 Materials With Exercises

Example 3.10 Determine which of the following expressions are equal tob 22 b,cc c2 bc1, (2 b),c. b 2cSolution:The only expression that is not equivalent isb 2c(sinceb 2 2 b ). Todemonstrate that, let us set b 0, c 1 and evaluate2 b 2 0 2,c 1b 2 0 2 2. Since 2 2 , we conclude that 2 b is not equivalent to b 2 .c 1ccThe expression 2 bc is equivalent because of the rules for addition of fractions.c1(2 b)is equivalent because of the rules for multiplication of fractions. b 2isccequivalent because we can replace2 b by its equivalent expression b 2 .Performing numerical operations results in equivalent expressionsThere are many operations one can perform on an algebraic expression to obtain an equivalent one.One of them is performing numerical operations according to the order of operations. For example,2 3x 5 x23x 6xExample 3.11 When possible, perform a numerical operation to create an equivalent expression. If nonumerical operation can be performed, clearly indicate so.4xa) 2 x 1b) c) 12 3x8d)m( 2 3)e)g) ( x)h)m2 3f) 2x ( 3)y i) ( 3m)( 2n)6 x3Solution:a) 2 x 1 21x 1x4x xb) Divide the numerator and denominator by 4 to reduce the fraction.8 2c) 12 3xSince multiplication of 3 and x has to be performed before addition,no numerical operation can be performed.m md) ( 23) 6me) 2 3 Since 3 must be first raised to m -th power, no numerical operation canbe performed.30