Question

Hãy viết phân thức \(\dfrac{3}{x-2}\)dưới dạng phân thức có mẫu số lần lượt là:

a/ x²-2x

b/ x²- 4

c/ 6- 3x

d/ (x-2)²

Answer 1

a) Do x² - 2x = x( x - 2 )

\(\Rightarrow\dfrac{3}{x-2}=\dfrac{3x}{x\left(x-2\right)}=\dfrac{3x}{x^2-2x}\)

b) Do x² - 4 = ( x - 2 )( x + 2 )

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

c) Do 6 - 3x = 3( 2 - x ) = -3( x - 2 )

\(\Rightarrow\dfrac{3}{x-2}=\dfrac{3.\left(-3\right)}{-3\left(x-2\right)}=-\dfrac{9}{6-3x}\)

d) Do ( x - 2 )² = ( x - 2 )( x - 2)

\(\Rightarrow\dfrac{3}{x-2}=\dfrac{3\left(x-2\right)}{\left(x-2\right)\left(x-2\right)}=\dfrac{3x-6}{\left(x-2\right)^2}\)