Toán Lớp 8: Rút gọn a)2x(1-x)+(x+3)(2x-3) b)(x+2)^2-(x+1)(x-1) c) x/x+2+2x/x-2-3x^2+4/x^2-4 giúp mik vs ạ

Question

Toán Lớp 8:  Rút gọn  a)2x(1-x)+(x+3)(2x-3)  b)(x+2)^2-(x+1)(x-1)  c) x/x+2+2x/x-2-3x^2+4/x^2-4 giúp mik vs ạ

thucquyenlan · Answer

Giải đáp+Lời giải và giải thích chi tiết:    a)   2x(1 - x) + (x + 3)(2x - 3)   = 2x - 2x^2 + (2x^2 - 3x + 6x - 9)   = 2x - 2x^2 + (2x^2 + 3x - 9)   = 2x - 2x^2 + 2x^2 + 3x - 9   = (2x^2 - 2^2) + (3x + 2x) - 9   = 5x - 9   b)   (x + 2)^2 - (x + 1)(x - 1)   = (x^2 + 2.x.2 + 2^2)  - (x^2 - 1)   = (x^2 + 4x + 4) - x^2 + 1   = x^2 + 4x + 4 - x^2 + 1   = (x^2 - x^2) + 4x + (4 + 1)   = 4x + 5   c)   x/{x + 2} + {2x}/{x - 2} - {3x^2 + 4}/{x^2 - 4}         (ĐKXĐ: x ne +- 2)   = x/{x + 2} + {2x}/{x - 2} - {3x^2 + 4}/{x^2 - 2^2}    = x/{x + 2} + {2x}/{x - 2} - {3x^2 + 4}/{(x - 2)(x + 2)}    = {x(x - 2)}/{(x - 2)(x + 2)} + {2x(x + 2)}/{(x - 2)(x + 2)} - {3x^2 + 4}/{(x - 2)(x + 2)}    = {x^2 - 2x}/{(x - 2)(x + 2)} + {2x^2 + 4x}/{(x - 2)(x + 2)} - {3x^2 + 4}/{(x - 2)(x + 2)}    = {x^2 - 2x + 2x^2 + 4x - (3x^2 + 4)}/{(x - 2)(x + 2)}    = {x^2 - 2x + 2x^2 + 4x - 3x^2 - 4}/{(x - 2)(x + 2)}    = {(x^2 + 2x^2 - 3x^2) + (4x - 2x) - 4}/{(x - 2)(x + 2)}    = {2x - 4}/{(x - 2)(x + 2)}    = {2(x - 2)}/{(x - 2)(x + 2)}    = 2/{x + 2}   #SunHee

ngocle44 · Answer

Giải đáp:   a) $=5x-9$   b) $=4x+5$   c) $= frac{-3x^4+9x^3-16x^2-8}{ left(x+2 right) left(x-2 right) left(-3x^2+x-2 right)}$   Lời giải và giải thích chi tiết:   a) $2x left(1-x right)+ left(x+3 right) left(2x-3 right)$   $=2x-2x^2+ left(x+3 right) left(2x-3 right)$   $=2x-2x^2+2x^2+3x-9$   $=2x+3x-9$   $=5x-9$   b) $ left(x+2 right)^2- left(x+1 right) left(x-1 right)$   $=x^2+4x+4- left(x+1 right) left(x-1 right)$   $=x^2+4x+4-x^2+1$   $=x^2-x^2+4x+4+1$   $=4x+4+1$   $=4x+5$   c) $ frac{x}{x+2}+ frac{2x}{x-2-3x^2}+ frac{4}{x^2-4}$   $= frac{x left(x-2 right) left(-3x^2+x-2 right)}{ left(x+2 right) left(x-2 right) left(-3x^2+x-2 right)}+ frac{2x left(x+2 right) left(x-2 right)}{ left(x+2 right) left(x-2 right) left(-3x^2+x-2 right)}+ frac{4 left(-3x^2+x-2 right)}{ left(x+2 right) left(x-2 right) left(-3x^2+x-2 right)}$   $= frac{x left(x-2 right) left(-3x^2+x-2 right)+2x left(x+2 right) left(x-2 right)+4 left(-3x^2+x-2 right)}{ left(x+2 right) left(x-2 right) left(-3x^2+x-2 right)}$   $= frac{-3x^4+9x^3-16x^2-8}{ left(x+2 right) left(x-2 right) left(-3x^2+x-2 right)}$