Câu 36 trang 34 Sách bài tập (SBT) Toán 8 tập 1

Hãy làm các phép chia sau :

Hãy làm các phép chia sau :

a. ({{7x + 2} over {3x{y^3}}}:{{14x + 4} over {{x^2}y}})

b. ({{8xy} over {3x - 1}}:{{12x{y^3}} over {5 - 15x}})

c. ({{27 - {x^3}} over {5x + 5}}:{{2x - 6} over {3x + 3}})

d. (left( {4{x^2} - 16} ight):{{3x + 6} over {7x - 2}})

e. ({{3{x^3} + 3} over {x - 1}}:left( {{x^2} - x + 1} ight))

Giải:

a. ({{7x + 2} over {3x{y^3}}}:{{14x + 4} over {{x^2}y}})( = {{7x + 2} over {3x{y^3}}}.{{{x^2}y} over {14x + 4}} = {{left( {7x + 2} ight){x^2}y} over {3x{y^3}.2left( {7x + 2} ight)}} = {x over {6{y^2}}})

b. ({{8xy} over {3x - 1}}:{{12x{y^3}} over {5 - 15x}})( = {{8xy} over {3x - 1}}.{{5 - 15x} over {12x{y^3}}} = {{8xyleft( {5 - 15x} ight)} over {left( {3x - 1} ight).12x{y^3}}} = {{ - 10left( {3x - 1} ight)} over {3left( {3x - 1} ight){y^2}}} = {{10} over {3{y^2}}})

c. ({{27 - {x^3}} over {5x + 5}}:{{2x - 6} over {3x + 3}})( = {{27 - {x^3}} over {5x + 5}}:{{3x + 3} over {2x - 6}} = {{left( {{3^3} - {x^3}} ight).3left( {x + 1} ight)} over {5left( {x + 1} ight).2left( {x - 3} ight)}})

( = {{ - 3left( {x - 3} ight)left( {{x^2} + 3x + 9} ight)} over {10left( {x - 3} ight)}} =  - {{3left( {{x^2} + 3x + 9} ight)} over {10}})

d. (left( {4{x^2} - 16} ight):{{3x + 6} over {7x - 2}})

( = left( {4{x^2} - 16} ight).{{7x - 2} over {3x + 6}} = {{4left( {x + 2} ight)left( {x - 2} ight)left( {7x - 2} ight)} over {3left( {x + 2} ight)}})

( = {{4left( {x - 2} ight)left( {7x - 2} ight)} over 3})

e. ({{3{x^3} + 3} over {x - 1}}:left( {{x^2} - x + 1} ight))( = {{3{x^3} + 3} over {x - 1}}.{1 over {{x^2} - x + 1}} = {{3left( {{x^3} + 1} ight)} over {left( {x - 1} ight)left( {{x^2} - x + 1} ight)}} = {{3left( {x + 1} ight)left( {{x^2} - x + 1} ight)} over {left( {x - 1} ight)left( {{x^2} - x + 1} ight)}})

( = {{3left( {x + 1} ight)} over {x - 1}})