Toán Lớp 8: Thực hiện phép tính a)4/x+2 + 3/x-2 + 5x+2/4+2x^2 b)1-2x/2x + 2x/2x-1 + 1/2x-4x^2

Question

Toán Lớp 8:  Thực hiện phép tính a)4/x+2 + 3/x-2 + 5x+2/4+2x^2 b)1-2x/2x + 2x/2x-1 + 1/2x-4x^2

thanoanghha · Answer

$a)$ $ dfrac{4}{x+2}+ dfrac{3}{x-2}+ dfrac{5x+2}{4+2x^2}$   $= dfrac{8 left(x-2 right) left(x^2+2 right)}{2 left(x+2 right) left(x-2 right) left(x^2+2 right)}+ dfrac{6 left(x+2 right) left(x^2+2 right)}{2 left(x+2 right) left(x-2 right) left(x^2+2 right)}+ dfrac{ left(5x+2 right) left(x+2 right) left(x-2 right)}{2 left(x+2 right) left(x-2 right) left(x^2+2 right)}$   $= dfrac{8 left(x-2 right) left(x^2+2 right)+6 left(x+2 right) left(x^2+2 right)+ left(5x+2 right) left(x+2 right) left(x-2 right)}{2 left(x+2 right) left(x-2 right) left(x^2+2 right)}$   $= dfrac{19x^3-2x^2+8x-16}{2 left(x+2 right) left(x-2 right) left(x^2+2 right)}$   $b)$ $ dfrac{1-2x}{2x}+ dfrac{2x}{2x-1}+ dfrac{1}{2x-4x^2}$   $= dfrac{ left(1-2x right) left(2x-1 right)}{2x left(2x-1 right)}+ dfrac{4x^2}{2x left(2x-1 right)}+ dfrac{-1}{2x left(2x-1 right)}$   $= dfrac{ left(1-2x right) left(2x-1 right)+4x^2-1}{2x left(2x-1 right)}$   $= dfrac{4x-2}{2x left(2x-1 right)}$   $= dfrac{1}{x}$