Question

Chứng minh đẳng thức: \(\dfrac{3x-2y}{5x-3y}=\dfrac{15x^2-xy-6y^2}{25x^2-9y^2}\)

Answer 1

Xét:

\(\left(3x-2y\right)\left(25x^2-9y^2\right)\)

\(=\left(3x-2y\right)\left(5x-3y\right)\left(5x+3y\right)\)

\(=\left(5x-3y\right)\left(15x^2+9xy-10xy-6y^2\right)\)

\(=\left(5x-3y\right)\left(15x^2-xy-6y^2\right)\)

Từ đó dễ dàng suy ra tích chéo = nhau => đpcm

Answer 2

ta có : \(VP=\dfrac{15x^2-xy-6y^2}{25x^2-9y^2}=\dfrac{\left(3x-2y\right)\left(5x+3y\right)}{\left(5x-3y\right)\left(5x+3y\right)}=\dfrac{3x-2y}{5x-3y}=VT\)