Bài 35 trang 50 sgk toán 8 tập 1

Bài 35 trang 50 sgk toán 8 tập 1

Thực hiện các phép tính:

Thực hiện các phép tính:

a)({{x + 1} over {x - 3}} - {{1 - x} over {x + 3}} - {{2xleft( {1 - x} ight)} over {9 - {x^2}}})

b)({{3x + 1} over {{{left( {x - 1} ight)}^2}}} - {1 over {x + 1}} + {{x + 3} over {1 - {x^2}}})

Hướng dẫn làm bài:

a)({{x + 1} over {x - 3}} - {{1 - x} over {x + 3}} - {{2xleft( {1 - x} ight)} over {9 - {x^2}}} = {{x + 1} over {x - 3}} + {{ - left( {1 - x} ight)} over {x + 3}} + {{2xleft( {1 - x} ight)} over { - left( {9 - {x^2}} ight)}})

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

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

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

( = {{2x + 6} over {left( {x - 3} ight)left( {x + 3} ight)}} = {{2left( {x + 3} ight)} over {left( {x - 3} ight)left( {x + 3} ight)}} = {2 over {x - 3}})

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

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

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

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

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

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

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