Bài 51 trang 58 sgk Toán 8 tập 1, Làm các phép tính sau:...

Làm các phép tính sau:

a) (left( {{{{x^2}} over {{y^2}}} + {y over x}} ight):left( {{x over {{y^2}}} – {1 over y} + {1 over x}} ight);)

b) (left( {{1 over {{x^2} + 4x + 4}} – {1 over {{x^2} – 4x + 4}}} ight):left( {{1 over {x + 2}} + {1 over {x – 2}}} ight))

Hướng dẫn làm bài:

a) (left( {{{{x^2}} over {{y^2}}} + {y over x}} ight):left( {{x over {{y^2}}} – {1 over y} + {1 over x}} ight) = {{{x^2}.x + y.{y^2}} over {x{y^2}}}:{{x{y^2}} over {{x^2} – xy + {y^2}}})

( = {{{x^3} + {y^3}} over {x{y^2}}}:{{{x^2} – xy + {y^2}} over {x{y^2}}} = {{{x^3} + {y^3}} over {x{y^2}}}.{{x{y^2}} over {{x^2} – xy + {y^2}}})

( = {{left( {x + y} ight)left( {{x^2} – xy + {y^2}} ight)x{y^2}} over {x{y^2}left( {{x^2} – xy + {y^2}} ight)}} = x + y)

b) (left( {{1 over {{x^2} + 4x + 4}} – {1 over {{x^2} – 4x + 4}}} ight):left( {{1 over {x + 2}} + {1 over {x – 2}}} ight))

( = left[ {{1 over {{{left( {x + 2} ight)}^2}}} – {1 over {{{left( {x – 2} ight)}^2}}}} ight]:{{x – 2 + x + 2} over {left( {x + 2} ight)left( {x – 2} ight)}})

( = {{{{left( {x – 2} ight)}^2} – {{left( {x + 2} ight)}^2}} over {{{left( {x + 2} ight)}^2}{{left( {x – 2} ight)}^2}}}.{{left( {x + 2} ight)left( {x – 2} ight)} over {2x}})

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

( = {{ – 8x} over {2x{{(x + 2)}^2}{{(x – 2)}^2}}} = {4 over {{{(x + 2)}^2}{{(x – 2)}^2}}})