Câu 19 trang 29 Sách bài tập (SBT) Toán 8 tập 1

Dùng quy tắc đổi dấu để tìm mẫu thức chung rồi thực hiện phép cộng:

Dùng quy tắc đổi dấu để tìm mẫu thức chung rồi thực hiện phép cộng:

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

b. ({{1 - 3x} over {2x}} + {{3x - 2} over {2x - 1}} + {{3x - 2} over {2x - 4{x^2}}})

c. ({1 over {{x^2} + 6x + 9}} + {1 over {6x - {x^2} - 9}} + {x over {{x^2} - 9}})

d. ({{{x^2} + 2} over {{x^3} - 1}} + {2 over {{x^2} + x + 1}} + {1 over {1 - x}})

e. ({x over {x - 2y}} + {x over {x + 2y}} + {{4xy} over {4{y^2} - {x^2}}})

Giải:

a. ({4 over {x + 2}} + {2 over {x - 2}} + {{5x - 6} over {4 - {x^2}}}) ( = {4 over {x + 2}} + {2 over {x - 2}} + {{6 - 5x} over {left( {x + 2} ight)left( {x - 2} ight)}})

(eqalign{  &  = {{4left( {x - 2} ight)} over {left( {x + 2} ight)left( {x - 2} ight)}} + {{2left( {x + 2} ight)} over {left( {x + 2} ight)left( {x - 2} ight)}} + {{6 - 5x} over {left( {x + 2} ight)left( {x - 2} ight)}} = {{4x - 8 + 2x + 4 + 6 - 5x} over {left( {x + 2} ight)left( {x - 2} ight)}}  cr  &  = {{x + 2} over {left( {x + 2} ight)left( {x - 2} ight)}} = {1 over {x - 2}} cr} )

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

(eqalign{  &  = {{left( {1 - 3x} ight)left( {2x - 1} ight)} over {2xleft( {2x - 1} ight)}} + {{left( {3x - 2} ight).2x} over {2xleft( {2x - 1} ight)}} + {{2 - 3x} over {2xleft( {2x - 1} ight)}}  cr  &  = {{2x - 1 - 6{x^2} + 3x + 6{x^2} - 4x + 2 - 3x} over {2xleft( {2x - 1} ight)}} = {{1 - 2x} over {2xleft( {2x - 1} ight)}} = {{ - left( {2x - 1} ight)} over {2xleft( {2x - 1} ight)}} = {{ - 1} over {2x}} cr} )

c. ({1 over {{x^2} + 6x + 9}} + {1 over {6x - {x^2} - 9}} + {x over {{x^2} - 9}})( = {1 over {{{left( {x + 3} ight)}^2}}} + {{ - 1} over {{{left( {x - 3} ight)}^2}}} + {x over {left( {x + 3} ight)left( {x - 3} ight)}})

(eqalign{  &  = {{{{left( {x - 3} ight)}^2}} over {{{left( {x + 3} ight)}^2}{{left( {x - 3} ight)}^2}}} + {{ - {{left( {x + 3} ight)}^2}} over {{{left( {x + 3} ight)}^2}{{left( {x - 3} ight)}^2}}} + {{xleft( {x + 3} ight)left( {x - 3} ight)} over {{{left( {x + 3} ight)}^2}{{left( {x - 3} ight)}^2}}}  cr  &  = {{{x^2} - 6x + 9 - {x^2} - 6x - 9 + {x^3} - 9x} over {{{left( {x + 3} ight)}^2}{{left( {x - 3} ight)}^2}}} = {{{x^3} - 21x} over {{{left( {x + 3} ight)}^2}{{left( {x - 3} ight)}^2}}} cr} )

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

(eqalign{  &  = {{{x^2} + 2} over {left( {x - 1} ight)left( {{x^2} + x + 1} ight)}} + {{2left( {x - 1} ight)} over {left( {x - 1} ight)left( {{x^2} + x + 1} ight)}} + {{ - left( {{x^2} + x + 1} ight)} over {left( {x - 1} ight)left( {{x^2} + x + 1} ight)}}  cr  &  = {{{x^2} + 2 + 2x - 2 - {x^2} - x - 1} over {left( {x - 1} ight)left( {{x^2} + x + 1} ight)}} = {{x - 1} over {left( {x - 1} ight)left( {{x^2} + x + 1} ight)}} = {1 over {{x^2} + x + 1}} cr} )

e. ({x over {x - 2y}} + {x over {x + 2y}} + {{4xy} over {4{y^2} - {x^2}}})( = {x over {x - 2y}} + {x over {x + 2y}} + {{ - 4xy} over {left( {x + 2y} ight)left( {x - 2y} ight)}})

(eqalign{  &  = {{xleft( {x + 2y} ight)} over {left( {x - 2y} ight)left( {x + 2y} ight)}} + {{xleft( {x - 2y} ight)} over {left( {x - 2y} ight)left( {x + 2y} ight)}} + {{ - 4xy} over {left( {x - 2y} ight)left( {x + 2y} ight)}}  cr  &  = {{{x^2} + 2xy + {x^2} - 2xy - 4xy} over {left( {x - 2y} ight)left( {x + 2y} ight)}} = {{2{x^2} - 4xy} over {left( {x - 2y} ight)left( {x + 2y} ight)}} = {{2xleft( {x - 2y} ight)} over {left( {x - 2y} ight)left( {x + 2y} ight)}}  cr  &  = {{2x} over {x + 2y}} cr} )