Toán Lớp 8: a)(2-x).(2+x)/x^3+8+x-2/x^2-2x+4+2x/x+2 b)7x+1/x-3-2.(x-14)/3-x

Question

Toán Lớp 8:  a)(2-x).(2+x)/x^3+8+x-2/x^2-2x+4+2x/x+2 b)7x+1/x-3-2.(x-14)/3-x

behocgioitoan · Answer

Giải đáp:   a) $ dfrac{(2-x)(2+x)}{x^3+8}+ dfrac{x-2}{x^2-2x+4}+ dfrac{2x}{x+2}= dfrac{2x}{x+2}$   b) $ dfrac{7x+1}{x-3}- dfrac{2(x-14)}{3-x}=9$   Lời giải và giải thích chi tiết:   a)   $ dfrac{(2-x)(2+x)}{x^3+8}+ dfrac{x-2}{x^2-2x+4}+ dfrac{2x}{x+2}  , , ,(x ne-2) = dfrac{(2-x)(2+x)}{(x+2)(x^2-2x+4)}+ dfrac{x-2}{x^2-2x+4}+ dfrac{2x}{x+2}  = dfrac{4-x^2+(x-2)(x+2)+2x(x^2-2x+4)}{(x+2)(x^2-2x+4)}  = dfrac{4-x^2+x^2-4+2x^3-4x^2+8x}{(x+2)(x^2-2x+4)}  = dfrac{2x^3-4x^2+8x}{(x+2)(x^2-2x+4)}  = dfrac{2x(x^2-2x+4)}{(x+2)(x^2-2x+4)}  = dfrac{2x}{x+2}$   b)   $ dfrac{7x+1}{x-3}- dfrac{2(x-14)}{3-x} , , ,(x ne3)  = dfrac{7x+1}{x-3}+ dfrac{2(x-14)}{x-3}  = dfrac{7x+1+2x-28}{x-3}  = dfrac{9x-27}{x-3}  = dfrac{9(x-3)}{x-3}  =9$