Question

Rút gọn phân thức:

1. 2x^2+4x/3x+6

2. 3x^2y^3/6xy

3. x^2 + 2x +1/2x+2

4. 9-x/x-9

5. -x^2+4/2x-4

Answer 1

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

2. \(\dfrac{3x^2y^3}{6xy}=\dfrac{xy^23xy}{2.3xy}=\dfrac{xy^2}{2}\)

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

4. \(\dfrac{9-x}{x-9}=\dfrac{9-x}{-\left(9-x\right)}=\dfrac{1}{-1}=-1\)

5. \(\dfrac{-x^2+4}{2x-4}=\dfrac{-\left(x^2-4\right)}{2.\left(x-2\right)}=\dfrac{-\left(x-2\right).\left(x-2\right)}{2.\left(x-2\right)}=\dfrac{-\left(x+2\right)}{2}\)