Question

Rút gọn:

a) \(\sqrt{\dfrac{9x^2}{25}}\) + \(\dfrac{1}{5}x\) (x<0).

b) 2xy . \(\sqrt{\dfrac{9x^2}{y^6}}-\sqrt{\dfrac{49x^2}{y^2}}\) (x<0; y>0).

c) \(\dfrac{1}{a-b}.\sqrt{a^6.\left(a-b\right)^2}\) (a<b<0).

Answer 1

a) \(\sqrt{\dfrac{9x^2}{25}}+\dfrac{1}{5}x\) (x<0)

=\(\dfrac{-3x}{5}+\dfrac{x}{5}\) (vì x<0)

=\(\dfrac{-2x}{5}\)

b)2xy\(\sqrt{\dfrac{9x^2}{y^6}}-\sqrt{\dfrac{49x^2}{y^2}}\) (x<0 , y>0)

=2xy\(\dfrac{-3x}{y^3}+\dfrac{7x}{y}\)(vì x<y<0)

=\(\dfrac{-6x}{y^2}+\dfrac{7xy}{y^2}\)

=\(\dfrac{7xy-6x}{y^2}\)

c) \(\dfrac{1}{ab}\sqrt{a^6\left(a-b\right)^2}\) (a<b<0)

=\(\dfrac{1}{ab}\sqrt{a^6}\sqrt{\left(a-b\right)^2}\)

=\(\dfrac{1}{ab}\left(-a^3\right)\left(b-a\right)\) (vì a<b<0)

=\(\dfrac{\left(a-b\right)a^3}{a-b}\)

=a³