*Restrictions are numbers that make a denominator=0.
Example 1- Find the Restriction
2x/x-3 x-3=0
x=3. Because x does not equal 3, 3 is the restriction.
Example 2- Find the Restriction
3x-4/x^2+5x+6(Factor First) 3x-4/(x+2)(x+3)
x+2=0 x+3=0
x=-2,-3
x does not equal -2 or -3 so the restrictions are -2 and -3.
Simplifying Rational Expressions
*When you simplify you must factor first!
Example 3- Simplify and find Restrictions
x^2+7x+12/x^2-16=(x+3)(x+4)/(x-4)(x+4)(Simplify by removing (x+4) from the numerator and denominator) (x+3)/(x-4) x does not equal 4 or -4 so those are your restrictions. Answer= x+3/x-4 with restrictions of 4 and -4.
Section 12.2- Rational Expressions
Review- Simplify
36m^6n^2/20m^3n^5= 9m^3/5n^3
Restrictions of Excluded Values
*Restrictions are numbers that make a denominator=0.Example 1- Find the Restriction
2x/x-3x-3=0
x=3. Because x does not equal 3, 3 is the restriction.
Example 2- Find the Restriction
3x-4/x^2+5x+6(Factor First)3x-4/(x+2)(x+3)
x+2=0 x+3=0
x=-2,-3
x does not equal -2 or -3 so the restrictions are -2 and -3.
Simplifying Rational Expressions
*When you simplify you must factor first!Example 3- Simplify and find Restrictions
x^2+7x+12/x^2-16=(x+3)(x+4)/(x-4)(x+4)(Simplify by removing (x+4) from the numerator and denominator)
(x+3)/(x-4) x does not equal 4 or -4 so those are your restrictions.
Answer= x+3/x-4 with restrictions of 4 and -4.