Lesson Worksheet: Multiplying and Dividing Rational Functions Mathematics • 10th Grade

In this worksheet, we will practice multiplying and dividing rational functions.


Simplify the function 𝑛(π‘₯)=2π‘₯+2Γ—π‘₯+6π‘₯+82π‘₯, and determine its domain.

  • A𝑛(π‘₯)=π‘₯+4π‘₯, domain = β„βˆ’{0,βˆ’2}
  • B𝑛(π‘₯)=π‘₯+4π‘₯, domain = ℝ
  • C𝑛(π‘₯)=π‘₯π‘₯+4, domain = β„βˆ’{0}
  • D𝑛(π‘₯)=π‘₯+2π‘₯, domain = β„βˆ’{0,βˆ’2}
  • E𝑛(π‘₯)=π‘₯+2π‘₯, domain = ℝ


Given that 𝑛(π‘₯)=π‘₯+9π‘₯βˆ’6, 𝑛(π‘₯)=9π‘₯+81π‘₯βˆ’6, and 𝑛(π‘₯)=𝑛(π‘₯)÷𝑛(π‘₯), identify the domain of 𝑛(π‘₯).

  • Aβ„βˆ’{βˆ’6}
  • Bβ„βˆ’{3,6}
  • Cβ„βˆ’{0,6}
  • Dβ„βˆ’{6}
  • Eβ„βˆ’{βˆ’6,βˆ’3}


Simplify the function 𝑛(π‘₯)=π‘₯+5π‘₯+9π‘₯+20Γ—π‘₯+15π‘₯+547π‘₯+69π‘₯+54, and determine its domain.

  • A𝑛(π‘₯)=π‘₯βˆ’6(π‘₯+4)(7π‘₯+6), domain =β„βˆ’ο¬βˆ’4,βˆ’67
  • B𝑛(π‘₯)=π‘₯βˆ’6(π‘₯βˆ’4)(7π‘₯βˆ’6), domain =β„βˆ’ο¬βˆ’9,βˆ’5,βˆ’4,βˆ’67
  • C𝑛(π‘₯)=π‘₯βˆ’6(π‘₯+4)(7π‘₯+6), domain =β„βˆ’ο¬βˆ’9,βˆ’5,βˆ’4,βˆ’67
  • D𝑛(π‘₯)=π‘₯+6(π‘₯+4)(7π‘₯+6), domain =β„βˆ’ο¬βˆ’4,βˆ’67
  • E𝑛(π‘₯)=π‘₯+6(π‘₯+4)(7π‘₯+6), domain =β„βˆ’ο¬βˆ’9,βˆ’5,βˆ’4,βˆ’67


Determine the domain of the function 𝑛(π‘₯)=π‘₯βˆ’π‘₯βˆ’6π‘₯βˆ’4Γ·2π‘₯βˆ’6π‘₯βˆ’4π‘₯+4.

  • Aβ„βˆ’{βˆ’3,βˆ’2}
  • Bℝ
  • Cβ„βˆ’{βˆ’2,2}
  • Dβ„βˆ’{βˆ’2,2,3}
  • Eβ„βˆ’{βˆ’3,βˆ’2,2}


Determine the domain of the function 𝑛(π‘₯)=3π‘₯βˆ’15π‘₯βˆ’6Γ·6π‘₯βˆ’304π‘₯βˆ’24.

  • Aβ„βˆ’{βˆ’6,βˆ’5}
  • Bβ„βˆ’{5,6}
  • Cβ„βˆ’{6}
  • Dβ„βˆ’{5}
  • Eℝ


Given the function 𝑛(π‘₯)=π‘₯βˆ’6π‘₯βˆ’15π‘₯+54Γ—π‘₯βˆ’3π‘₯βˆ’282π‘₯βˆ’15π‘₯+7, evaluate 𝑛(7), if possible.

  • Aβˆ’12
  • Bundefined
  • Cβˆ’188
  • Dβˆ’2


Simplify the function 𝑛(π‘₯)=9π‘₯+72π‘₯+1Γ·9π‘₯+725π‘₯+5, and determine its domain.

  • A𝑛(π‘₯)=581, domain =β„βˆ’{1,8}
  • B𝑛(π‘₯)=815, domain =β„βˆ’{βˆ’8}
  • C𝑛(π‘₯)=25, domain =ℝ
  • D𝑛(π‘₯)=5, domain =β„βˆ’{βˆ’1,βˆ’8}
  • E𝑛(π‘₯)=15, domain =β„βˆ’{βˆ’1}


Simplify the function 𝑛(π‘₯)=π‘₯+3432π‘₯+14π‘₯Γ—π‘₯+3π‘₯βˆ’7π‘₯+49, and determine its domain.

  • A𝑛(π‘₯)=π‘₯2(π‘₯+3), domain =β„βˆ’{βˆ’7,0}
  • B𝑛(π‘₯)=π‘₯+32π‘₯, domain =β„βˆ’{0}
  • C𝑛(π‘₯)=π‘₯+32π‘₯, domain =β„βˆ’{βˆ’7,0}
  • D𝑛(π‘₯)=2π‘₯π‘₯+3, domain =β„βˆ’{0}
  • E𝑛(π‘₯)=2π‘₯π‘₯+3, domain =β„βˆ’{βˆ’7,0}


Simplify the function 𝑛(π‘₯)=π‘₯+16π‘₯+64π‘₯+8π‘₯Γ—7π‘₯βˆ’5664βˆ’π‘₯, and determine its domain.

  • A𝑛(π‘₯)=βˆ’7π‘₯, domain =β„βˆ’{0}
  • B𝑛(π‘₯)=βˆ’7π‘₯, domain =β„βˆ’{βˆ’8,0,8}
  • C𝑛(π‘₯)=βˆ’17π‘₯, domain =β„βˆ’{βˆ’8,0,8}
  • D𝑛(π‘₯)=7π‘₯, domain =β„βˆ’{βˆ’8,0,8}
  • E𝑛(π‘₯)=7π‘₯, domain =β„βˆ’{0}


Given that 𝑓(π‘₯)=π‘₯+9π‘₯+14π‘₯βˆ’4Γ·π‘₯βˆ’49π‘₯βˆ’2π‘₯ and 𝑓(π‘Ž)=4, find the value of π‘Ž.

  • Aβˆ’283
  • B283
  • Cβˆ’285
  • D285
  • Eβˆ’73

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