Question

a) \(\dfrac{x^2-16}{4x-x^2}\)

b) \(\dfrac{x^2+4x+3}{2x+6}\)

c) \(\dfrac{5\left(x-y\right)-3\left(y-x\right)}{10\left(x-y\right)}\)

d) \(\dfrac{2ax^2-4ax+2a}{5b-5bx^2}\)

e) \(\dfrac{\left(x+y\right)^2-z^2}{x+y+z}\)

f) \(\dfrac{4x^2-4xy}{5x^3-5x^2y}\)

Nguyễn Huy Tú, Hoàng Ngọc Anh, Toshiro Kiyoshi,...

Answer 1

a) \(\dfrac{x^2-16}{4x-x^2}=\dfrac{\left(x-4\right)\left(x+4\right)}{x\left(4-x\right)}=\dfrac{\left(x-4\right)\left(x+4\right)}{x\left[-\left(x-4\right)\right]}\)

\(=\dfrac{\left(-1\right)\left(x+4\right)}{x}=\dfrac{-x-4}{x}\)

b) \(\dfrac{x^2+4x+3}{2x+6}=\dfrac{x^2+3x+x+3}{2\left(x+3\right)}=\dfrac{x\left(x+3\right)+\left(x+3\right)}{2\left(x+3\right)}\)

\(=\dfrac{\left(x+1\right)\left(x+3\right)}{2\left(x+3\right)}=\dfrac{x+1}{2}\)

c) \(\dfrac{5\left(x-y\right)-3\left(y-x\right)}{10\left(x-y\right)}=\dfrac{5\left(x-y\right)+3\left(x-y\right)}{10\left(x-y\right)}\)

\(=\dfrac{8\left(x-y\right)}{10\left(x-y\right)}=\dfrac{8}{10}=\dfrac{4}{5}\)

d) \(\dfrac{2ax^2-4ax+2a}{5b-5bx^2}=\dfrac{2a\left(x^2-2x+1\right)}{5b\left(1-x^2\right)}=\dfrac{2a\left(x-1\right)^2}{5b\left[-\left(x-1\right)\right]\left(1+x\right)}\)

\(=\dfrac{2a\left[-\left(x-1\right)\right]}{5b\left(1+x\right)}=-\dfrac{2ax-2a}{50\left(1+x\right)}=-\dfrac{-\left(2a-2ax\right)}{5b\left(1+x\right)}-\dfrac{2a-2ax}{5b-5bx}\)

e) \(\dfrac{\left(x+y\right)^2-z^2}{x+y+z}=\dfrac{\left(x+y-z\right)\left(x+y+z\right)}{x+y+z}=z+y-z\)

f) \(\dfrac{4x^2-4xy}{5x^3-5x^2y}=\dfrac{4x\left(x-y\right)}{5x^2\left(x-y\right)}=\dfrac{4x}{5x^2}=\dfrac{4}{5x}\)

Answer 2

a, \(\dfrac{x^2-16}{4x-x^2}=\dfrac{\left(x-4\right)\left(x+4\right)}{x\left(4-x\right)}=\dfrac{-x-4}{x}=-1-\dfrac{4}{x}\)

b, \(\dfrac{x^2+4x+3}{2x+6}=\dfrac{x^2+x+3x+3}{2\left(x+3\right)}\)

\(=\dfrac{x\left(x+1\right)+3\left(x+1\right)}{2\left(x+3\right)}=\dfrac{\left(x+1\right)\left(x+3\right)}{2\left(x+3\right)}\)

\(=\dfrac{x+1}{2}\)

c,\(\dfrac{5\left(x-y\right)-3\left(y-x\right)}{10\left(x-y\right)}=\dfrac{5\left(x-y\right)+3\left(x-y\right)}{10\left(x-y\right)}\)

\(=\dfrac{8\left(x-y\right)}{10\left(x-y\right)}=\dfrac{4}{5}\)

d, \(\dfrac{2ax^2-4ax+2a}{5b-5bx^2}=\dfrac{a\left(2x^2-4x+2\right)}{-5b\left(x^2-1\right)}\)

\(=\dfrac{2a\left(x-1\right)^2}{-5b\left(x-1\right)\left(x+1\right)}=\dfrac{2a\left(x-1\right)}{-5b\left(x+1\right)}\)

e, \(\dfrac{\left(x+y\right)^2-z^2}{x+y+z}=\dfrac{\left(x+y+z\right)\left(x+y-z\right)}{x+y+z}=x+y-z\)

f, \(\dfrac{4x^2-4xy}{5x^3-5x^2y}=\dfrac{4x\left(x-y\right)}{5x^2\left(x-y\right)}=\dfrac{4}{5x}\)

Chúc bạn học tốt!!!