Câu 9 trang 26 Sách bài tập (SBT) Toán 8 tập 1

Rút gọn các phân thức sau:

Rút gọn các phân thức sau:

a. ({{14x{y^5}left( {2x - 3y} ight)} over {21{x^2}y{{left( {2x - 3y} ight)}^2}}})

b. ({{8xy{{left( {3x - 1} ight)}^3}} over {12{x^3}left( {1 - 3x} ight)}})

c. ({{20{x^2} - 45} over {{{left( {2x + 3} ight)}^2}}})

d.({{5{x^2} - 10xy} over {2{{left( {2y - x} ight)}^3}}})

e. ({{80{x^3} - 125x} over {3left( {x - 3} ight) - left( {x - 3} ight)left( {8 - 4x} ight)}})

f. ({{9 - {{left( {x + 5} ight)}^2}} over {{x^2} + 4x + 4}})

g. ({{32x - 8{x^2} + 2{x^3}} over {{x^3} + 64}})

h. ({{5{x^3} + 5x} over {{x^4} - 1}})

i. ({{{x^2} + 5x + 6} over {{x^2} + 4x + 4}})

Giải:

a. ({{14x{y^5}left( {2x - 3y} ight)} over {21{x^2}y{{left( {2x - 3y} ight)}^2}}}) (= {{2{y^4}} over {3xleft( {2x - 3y} ight)}})

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

c.  ({{20{x^2} - 45} over {{{left( {2x + 3} ight)}^2}}}) ( = {{5left( {4{x^2} - 9} ight)} over {{{left( {2x + 3} ight)}^2}}} = {{5left( {2x + 3} ight)left( {2x - 3} ight)} over {{{left( {2x + 3} ight)}^2}}} = {{5left( {2x - 3} ight)} over {2x + 3}})

d. ({{5{x^2} - 10xy} over {2{{left( {2y - x} ight)}^3}}}) ( = {{ - 5xleft( {2y - x} ight)} over {2{{left( {2y - x} ight)}^3}}} = {{ - 5x} over {2{{left( {2y - x} ight)}^2}}})

e. ({{80{x^3} - 125x} over {3left( {x - 3} ight) - left( {x - 3} ight)left( {8 - 4x} ight)}}) ( = {{5xleft( {16{x^2} - 25} ight)} over {left( {x - 3} ight)left( {3 - 8 + 4x} ight)}} = {{5xleft( {16{x^2} - 25} ight)} over {left( {x - 3} ight)left( {4x - 5} ight)}} = {{5xleft( {4x + 5} ight)} over {x - 3}})

f. ({{9 - {{left( {x + 5} ight)}^2}} over {{x^2} + 4x + 4}}) ( = {{left( {3 + x + 5} ight)left( {3 - x - 5} ight)} over {{{left( {x + 2} ight)}^2}}} = {{ - left( {8 + x} ight)left( {x + 2} ight)} over {{{left( {x + 2} ight)}^2}}} = {{ - left( {8 + x} ight)} over {x + 2}})

g. ({{32x - 8{x^2} + 2{x^3}} over {{x^3} + 64}}) ( = {{2xleft( {16 - 4x + {x^2}} ight)} over {left( {x + 4} ight)left( {{x^2} - 4x + 16} ight)}} = {{2x} over {x + 4}})

h. ({{5{x^3} + 5x} over {{x^4} - 1}})( = {{5xleft( {{x^2} + 1} ight)} over {left( {{x^2} - 1} ight)left( {{x^2} + 1} ight)}} = {{5x} over {{x^2} - 1}})

i. ({{{x^2} + 5x + 6} over {{x^2} + 4x + 4}}) ( = {{{x^2} + 2x + 3x + 6} over {{{left( {x + 2} ight)}^2}}} = {{xleft( {x + 2} ight) + 3left( {x + 2} ight)} over {{{left( {x + 2} ight)}^2}}} = {{left( {x + 2} ight)left( {x + 3} ight)} over {{{left( {x + 2} ight)}^2}}} = {{x + 3} over {x + 2}})