The excluded value of the rational expression
(d) 1
(c) 4
(b) 2
(a) 8
Answers
Answer:
be reduced further?
Simplify Rational Expressions
You have gained experience working with rational functions so far. In this section, you will continue simplifying rational expressions by factoring.
To simplify a rational expression means to reduce the fraction into its lowest terms.
To do this, you will need to remember a property about multiplication.
For all real values
a and b
, and
b≠0,abb=a
.
Let's simplify the following rational expression:
x2−2x+18x−8
Factor both pieces of the rational expression and reduce.
x2−2x+18x−8→(x−1)(x−1)8(x−1)x2−2x+18x−8=x−18
Finding Excluded Values of Rational Expressions
As stated in a previous Concept, excluded values are also called points of discontinuity. These are the values that make the denominator equal to zero and are not part of the domain.
Find the excluded values of
2x+1x2−x−6
.
Factor the denominator of the rational expression.
2x+1x2−x−6=2x+1(x+2)(x−3)
Find the value that makes each factor equal zero.
x=−2,x=3
These are excluded values of the domain of the rational expression.
Let's use simplifying rational expressions to solve the following real-world application:
The gravitational force between two objects in given by the formula
F=G(m1m2)(d2)
. The gravitation constant is given by
G=6.67×10−11(N⋅m2/kg2)
. The force of attraction between the Earth and the Moon is
F=2.0×1020 N
(with masses of
m1=5.97×1024 kg
for the Earth and
m2=7.36×1022 kg
for the Moon).
What is the distance between the Earth and the Moon?
Let's start with the Law of Gravitation formula.Now plug in the known values.Multiply the masses together.Cancel
Answer:-
The excluded values are the values that are excluded or left out. The rational expression of values is equal to =0