Definitions
& Facts
& Facts
What are three techniques used to factor? Bonus 50 points if you can mention 4 methods.
GCF
X method
Box method
*Difference of Squares (50 bonus points if mentioned)
Simplify:
(4x^3)/(12x)
(x^2)/(3)
(9x^2y)/(15x)*(5x^3)/(12y^3)
(x^4)/(4y^2)
(8x)/(15y^2)+(2x+5y)/(15y^2)
(2x+y)/(3y^2)
State the restrictions of this expression:
(x)/(5x^2-25x)
0 and 5
Give the definition of a rational expression.
When two polynomials are in the form of a fraction, one in the numerator and the other in the denominator.
Simplify:
(3n^2+27n)/(n+9)
3n
(v+3)/(v-6)*(v^2-36)/(3v+9)
(v+6)/(3)
(10x+6)/(3x-15)-(x+3)/(3x-15)
(3x+1)/(x-5)
State the restrictions:
(2x-14)/(2x^2-98)
-7 and 7
When you have common factors in the numerator and the denominator then you can __________ them out.
Cancel / Divide
Simplify:
(x^2-9x+20)/(x^2+x-30)
(x-4)/(x+6)
(x^2+6x-40)/(7x-28)*(21)/(x+9)
(3(x+10))/(x+9)
(2x)/(6x^2+12x)-(x-2)/(6x^2+12x)
1/(6x)
True or false: We get our restricted values from our denominator once it is factored (before we cancel out any common factors)
TRUE!
Before we cancel any common factors, we need to identify which values would make our denominator equal to zero.
What needs to be true in order to add and subtract rational expressions?
Common Denominator
Simplify:
(m^2-16)/(4m^3-28m^2+48m)
(m+4)/(4m(m-3))
(5m^2-13m+8)/(m-7)*(1)/(5m-8)
(m-1)/(m-7)
(4)/(a^2+3a+2)+(5a+1)/(a^2+3a+2)
(5)/(a+2)
Is -15 a restriction of this expression?
50 Bonus points: name all the restrictions
(2x+10)/(15x(x-18)(x+5))
-15 is NOT a restriction because if we input the value into the denominator it will give us a number and NOT zero.
* 0, 18 and -5 are the restrictions (50 bonus points)
Restrictions are values that set the ___________ equal to ______.
Restrictions are values that set the DENOMINATOR equal to ZERO.
Simplify:
(45-5w)/(3w^2-28w+9)
(-5)/(3w-1)
(3x(x^2+16x+60))/(2x+16)*(x+8)/(9x^3+54x^2)
(x+10)/(6x)
(10x+20)/(4x^2+26x+40)-(2x-12)/(4x^2+26x+40)
(4)/(2x+5)
State the restrictions:
(3x+15)/(x^2-3x-40)
8 and -5