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

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

Q1:

Simplify the function ๐‘›(๐‘ฅ)=2๐‘ฅ+2ร—๐‘ฅ+6๐‘ฅ+82๐‘ฅ๏Šจ, and determine its domain.

  • A๐‘›(๐‘ฅ)=๐‘ฅ+4๐‘ฅ, domain = โ„โˆ’{0,โˆ’2}
  • B๐‘›(๐‘ฅ)=๐‘ฅ+4๐‘ฅ, domain = โ„
  • C๐‘›(๐‘ฅ)=๐‘ฅ๐‘ฅ+4, domain = โ„โˆ’{0}
  • D๐‘›(๐‘ฅ)=๐‘ฅ+2๐‘ฅ, domain = โ„โˆ’{0,โˆ’2}
  • E๐‘›(๐‘ฅ)=๐‘ฅ+2๐‘ฅ, domain = โ„

Q2:

Given that ๐‘›(๐‘ฅ)=๐‘ฅ+9๐‘ฅโˆ’6๏Šง, ๐‘›(๐‘ฅ)=9๐‘ฅ+81๐‘ฅโˆ’6๏Šจ, and ๐‘›(๐‘ฅ)=๐‘›(๐‘ฅ)รท๐‘›(๐‘ฅ)๏Šง๏Šจ, identify the domain of ๐‘›(๐‘ฅ).

  • Aโ„โˆ’{โˆ’6}
  • Bโ„โˆ’{3,6}
  • Cโ„โˆ’{0,6}
  • Dโ„โˆ’{6}
  • Eโ„โˆ’{โˆ’6,โˆ’3}

Q3:

Simplify the function ๐‘›(๐‘ฅ)=๐‘ฅ+5๐‘ฅ+9๐‘ฅ+20ร—๐‘ฅ+15๐‘ฅ+547๐‘ฅ+69๐‘ฅ+54๏Šจ๏Šจ๏Šจ, and determine its domain.

  • A๐‘›(๐‘ฅ)=๐‘ฅโˆ’6(๐‘ฅ+4)(7๐‘ฅ+6), domain =โ„โˆ’๏ฌโˆ’4,โˆ’67๏ธ
  • B๐‘›(๐‘ฅ)=๐‘ฅโˆ’6(๐‘ฅโˆ’4)(7๐‘ฅโˆ’6), domain =โ„โˆ’๏ฌโˆ’9,โˆ’5,โˆ’4,โˆ’67๏ธ
  • C๐‘›(๐‘ฅ)=๐‘ฅโˆ’6(๐‘ฅ+4)(7๐‘ฅ+6), domain =โ„โˆ’๏ฌโˆ’9,โˆ’5,โˆ’4,โˆ’67๏ธ
  • D๐‘›(๐‘ฅ)=๐‘ฅ+6(๐‘ฅ+4)(7๐‘ฅ+6), domain =โ„โˆ’๏ฌโˆ’4,โˆ’67๏ธ
  • E๐‘›(๐‘ฅ)=๐‘ฅ+6(๐‘ฅ+4)(7๐‘ฅ+6), domain =โ„โˆ’๏ฌโˆ’9,โˆ’5,โˆ’4,โˆ’67๏ธ

Q4:

Determine the domain of the function ๐‘›(๐‘ฅ)=๐‘ฅโˆ’๐‘ฅโˆ’6๐‘ฅโˆ’4รท2๐‘ฅโˆ’6๐‘ฅโˆ’4๐‘ฅ+4๏Šจ๏Šจ๏Šจ.

  • Aโ„โˆ’{โˆ’3,โˆ’2}
  • Bโ„
  • Cโ„โˆ’{โˆ’2,2}
  • Dโ„โˆ’{โˆ’2,2,3}
  • Eโ„โˆ’{โˆ’3,โˆ’2,2}

Q5:

Determine the domain of the function ๐‘›(๐‘ฅ)=3๐‘ฅโˆ’15๐‘ฅโˆ’6รท6๐‘ฅโˆ’304๐‘ฅโˆ’24.

  • Aโ„โˆ’{โˆ’6,โˆ’5}
  • Bโ„โˆ’{5,6}
  • Cโ„โˆ’{6}
  • Dโ„โˆ’{5}
  • Eโ„

Q6:

Given the function ๐‘›(๐‘ฅ)=๐‘ฅโˆ’6๐‘ฅโˆ’15๐‘ฅ+54ร—๐‘ฅโˆ’3๐‘ฅโˆ’282๐‘ฅโˆ’15๐‘ฅ+7๏Šจ๏Šจ๏Šจ, evaluate ๐‘›(7), if possible.

  • Aโˆ’12
  • Bundefined
  • Cโˆ’188
  • Dโˆ’2

Q7:

Simplify the function ๐‘›(๐‘ฅ)=9๐‘ฅ+72๐‘ฅ+1รท9๐‘ฅ+725๐‘ฅ+5, and determine its domain.

  • A๐‘›(๐‘ฅ)=581, domain =โ„โˆ’{1,8}
  • B๐‘›(๐‘ฅ)=815, domain =โ„โˆ’{โˆ’8}
  • C๐‘›(๐‘ฅ)=25, domain =โ„
  • D๐‘›(๐‘ฅ)=5, domain =โ„โˆ’{โˆ’1,โˆ’8}
  • E๐‘›(๐‘ฅ)=15, domain =โ„โˆ’{โˆ’1}

Q8:

Simplify the function ๐‘›(๐‘ฅ)=๐‘ฅ+3432๐‘ฅ+14๐‘ฅร—๐‘ฅ+3๐‘ฅโˆ’7๐‘ฅ+49๏Šฉ๏Šจ๏Šจ, and determine its domain.

  • A๐‘›(๐‘ฅ)=๐‘ฅ2(๐‘ฅ+3), domain =โ„โˆ’{โˆ’7,0}
  • B๐‘›(๐‘ฅ)=๐‘ฅ+32๐‘ฅ, domain =โ„โˆ’{0}
  • C๐‘›(๐‘ฅ)=๐‘ฅ+32๐‘ฅ, domain =โ„โˆ’{โˆ’7,0}
  • D๐‘›(๐‘ฅ)=2๐‘ฅ๐‘ฅ+3, domain =โ„โˆ’{0}
  • E๐‘›(๐‘ฅ)=2๐‘ฅ๐‘ฅ+3, domain =โ„โˆ’{โˆ’7,0}

Q9:

Simplify the function ๐‘›(๐‘ฅ)=๐‘ฅ+16๐‘ฅ+64๐‘ฅ+8๐‘ฅร—7๐‘ฅโˆ’5664โˆ’๐‘ฅ๏Šจ๏Šจ๏Šจ, and determine its domain.

  • A๐‘›(๐‘ฅ)=โˆ’7๐‘ฅ, domain =โ„โˆ’{0}
  • B๐‘›(๐‘ฅ)=โˆ’7๐‘ฅ, domain =โ„โˆ’{โˆ’8,0,8}
  • C๐‘›(๐‘ฅ)=โˆ’17๐‘ฅ, domain =โ„โˆ’{โˆ’8,0,8}
  • D๐‘›(๐‘ฅ)=7๐‘ฅ, domain =โ„โˆ’{โˆ’8,0,8}
  • E๐‘›(๐‘ฅ)=7๐‘ฅ, domain =โ„โˆ’{0}

Q10:

Given that ๐‘“(๐‘ฅ)=๐‘ฅ+9๐‘ฅ+14๐‘ฅโˆ’4รท๐‘ฅโˆ’49๐‘ฅโˆ’2๐‘ฅ๏Šจ๏Šจ๏Šจ๏Šจ and ๐‘“(๐‘Ž)=4, find the value of ๐‘Ž.

  • Aโˆ’283
  • B283
  • Cโˆ’285
  • D285
  • Eโˆ’73

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