Câu 36 trang 34 Sách bài tập 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}})