Toán Lớp 8: rút gọn các phân thức a, A= 5x^2-10xy/2(2y-x)^3 b, B= 16-(x+1)^2/x^2+10x+25 c, C= x^2+5x+6/x^2-4

TRẢ LỜI

1. Giải đáp:

   a,

   A= $\frac{5x^2-10xy}{2(2y-x)^3}$

     = $\frac{5x.x-5x.2y}{-2(x – 2y)^3}$

     = $\frac{5x(x – 2y)}{-2(x – 2y)^3}$

     = $\frac{5x}{-2(x – 2y)^2}$

   b,

   B= $\frac{16-(x + 1)^2}{x^2+10x+25}$

      = $\frac{4^2-(x+1)^2}{x^2+2.x.5+5^2}$

      = $\frac{[4 -(x +1)].[4+x+1]}{(x+5)^2}$

      = $\frac{(3-x)(x+5)}{(x+5)^2}$ 

      = $\frac{3 -x}{x + 5}$

   c,

   C= $\frac{x^2 + 5x + 6}{x^2 – 4}$ 

     = $\frac{x^2 + 2x + 3x + 6}{x^2 – 2^2}$

     = $\frac{x(x + 2) + 3(x + 2)}{(x – 2)(x + 2)}$

     = $\frac{(x + 3)(x + 2)}{(x -2)(x+2)}$

     = $\frac{x + 3}{x – 2}$ 

   Học tốt

    

    

   Trả lời
2. a)

   A=(5x^2-10xy)/(2(2y-x)^3)

   =(5x(x-2y))/(-2(x-2y)^3)

   =(5x)/((-2)(x-2y)^2)

   b)

   B=(16-(x+1)^2)/(x^2+10x+25)

   =(4^2-(x+1)^2)/(x+5)^2

   =((4-x-1)(4+x+1))/(x+5)^2

   =((3-x)(x+5))/(x+5)^2

   =(3-x)/(x+5)

   c)

   C=(x^2+5x+6)/(x^2-4)

   =(x^2+2x+3x+6)/(x^2-2^2)

   =((x^2+2x)+(3x+6))/((x-2)(x+2))

   =(x(x+2)+3(x+2))/((x-2)(x+2))

   =((x+3)(x+2))/((x-2)(x+2))

   =(x+3)/(x-2)

    

   Trả lời