Question

Dùng định nghĩa hai phân thức bằng nhau chứng minh các đẳng thức sau :

a) \(\dfrac{x^2y^3}{5}=\dfrac{7x^3y^4}{35xy}\)

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

c) \(\dfrac{3-x}{3+x}=\dfrac{x^2-6x+9}{9-x^2}\)

d) \(\dfrac{x^3-4x}{10-5x}=\dfrac{-x^2-2x}{5}\)

Answer 1

a. \(x^2y^3.35xy=5.7x^3y^4\)

\(\Leftrightarrow35x^3y^4=35x^3y^4\Rightarrowđpcm\)

\(b.x^2\left(x+2\right).\left(x+2\right)=x\left(x+2\right)^2.x\)

\(\Leftrightarrow x^2\left(x+2\right)^2=x^2\left(x+2\right)^2\Rightarrowđpcm\)

\(c.\left(3-x\right)\left(9-x^2\right)=\left(3+x\right)\left(x^2-6x+9\right)\)

\(\Leftrightarrow\left(3-x\right)\left(3-x\right)\left(3+x\right)=\left(3+x\right)\left(3-x\right)^2\)

\(\Leftrightarrow\left(3-x\right)^2\left(3+x\right)=\left(3-x\right)^2\left(3+x\right)\)

\(\Rightarrowđpcm\)

\(d.5\left(x^3-4x\right)=\left(10-5x\right)\left(-x^2-2x\right)\)

\(\Leftrightarrow5x^3-20x=5x^3-20x\Rightarrowđpcm\)