2.1/2.2 Multiplying and Dividing Rational Expressions – Worksheet MCR3U Jensen 1) State the restrictions for each function. a) b) c) d) 2) Simplify each expression and state all restrictions on . a) !!! ! ! !!"!!!" b) ! ! !!!!!" ! ! !!!!" c) !!! ! ! !!!!!" 3) Simplify and state the restrictions on the variables. a) !"! !!! × !"!! !! b) !"! ! !! × !"! !"! ! c) !! !! ÷ !! !"! ! d) !"!" !! ÷ !"! ! ! ! !"! ! 4) Simplify and state the restrictions on the variable. a) !" !!!" × !!!" ! b) !!! !!! × !!! !!!
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2.1/2.2 Multiplying and Dividing Rational Expressions – Worksheet MCR3U Jensen 1) State the restrictions for each function. a) b) c) d) 2) Simplify each expression and state all restrictions on 𝑥. a) !!!
!!!!"!!!" b) !
!!!!!!"!!!!!!"
c) !!!!!!!!!!"
3) Simplify and state the restrictions on the variables. a) !"!
!!!× !"!!
!! b) !"!
!
!!× !"!!"!!
c) !!!!÷ !!
!"!! d) !"!"
!!÷ !"!!!!
!"!!
4) Simplify and state the restrictions on the variable. a) !"
!!!"× !!!"
! b) !!!
!!!× !!!!!!
c) !!!!÷ !!!
!! d) !!!"
!!!"÷ !!!"
!!!
5) Simplify and state the restrictions on the variable. a) !!!
!"!!!!"!× !!!!!!!!"
b) !!!!"!!!!!
× !"!!
!!!!"
c) !
!!!"!!!"!!!
× !!!!!!!!!!"
d) !!!!!!!"!!!!!!!"
× !!!!!!
6) Simplify and state the restrictions on the variable a) !
!!!"!!!!!"
÷ !!!!!!"
b) !!!!!!"
÷ !!!!!!"
c) !!!!"!!!"!!!
÷ !!!!!!!"!"!!
d) !!!!!!!!"!!!!!!!
÷ !!!!!!
7) Simplify and state the restrictions on the variable a) !
!!!"!!!
∙ !!!!!!!!!!!"
b) !!!!!!!"!!!!!!
∙ !!!!!!!!!!!!!"
c) !
!!!!!!!!!
÷ !!!!!!!
d) !!!!!!!"
!!!!!!!!"÷ !!!
!!!!!!
Answers 1) a) 𝑥 ≠ 3 b) 𝑥 ≠ −2 c) 𝑥 ≥ 1, 𝑥 ≠ 5 d) 𝑥 ≠ −3, 𝑥 ≠ −2 2) a) !