Denise G. answered • 04/17/19
Algebra, College Algebra, Prealgebra, Precalculus, GED, ASVAB Tutor
a) Explain in words how 2x2-x-6 over x3-2x2+3x-6 can be simplified to 2x+3 over x2+3
This rational expression can be simplified by factoring both the numerator and the denominator and then cancelling out the common factors. The common factor in both is (x-2) Once cancelled, the simplified expression is the result.
b) Evaluate 2x2-x-6 over x3-2x2+3x-6 and 2x+3 over x2+3 for x= -3, 0, and 3
2(-3)+3 = -6+3 = -3 = -1
(-3)2+3 9+3 12 4
2(0)+3 = 3 = 1
(0)2+3 3
2(3)+3 = 6+3 = 9 = 3
(3)2+3 9+3 12 4
c) Evaluate 2x3-x-6 over x3-2x2+3x-6 and 2x+3 over x2+3 for x=2
At x=2, there is no solution. It is a restricted value, which means it gives you a 0 in the denominator.
d) Explain the relationship between x=2 and the factor x-2
Of you set the factor x-2=0 and solve, you get the zero or the x intercept, which is 2.
e) Simplfy the expression 2x2-5x-12 over x3- 4x2+ 3x-12 and state any excluded values for x.
Factoring both the numerator and denominator you get the following
(2x+3)(x-4)
(x2+3)(x-4)
(x-4) is common in both and can cancel out. The final solution is:
(2x+3)
(x2+3)
The excluded value comes from setting x-4=0 and solving. x=4 is the excluded value, it gives 0 in the denominator.
