Expanding Exponent Expressions

[thomas49th]

Hi, I don know how to go about expanding things such as

$$3x\sqrt{3x-1}$$
apparently that equals 12x^{2} - 4x

i know that $$3x\sqrt{3x-1}$$ can be written as $$3x(3x-1)^{\frac{1}{2}}$$

but i don't know what to do. I can't remeber.

Thanks :)

 

[Snazzy]

$$3x\sqrt{3x-1} \neq 12x^2 - 4x$$

 

[thomas49th]

SORRY MY BAD I MENT $$2x\sqrt{3x-1}$$ = 12x^{2} - 4x

How do i get there?

Thanks :)

 

[Snazzy]

$$2x\sqrt{3x-1} \neq 12x^2 - 4x$$

 

[thomas49th]

SORRY. Ill start a bit further back
i have this:

$$x^{2}\frac{3}{2}(2x-1)^{-1}{2} + 2x\sqrt{3x-1}$$

and I don't know how it simplifies to

$$\frac{3x^{2} + 12x^{2} - 4x}{2\sqrt{3x-1}}$$I can't see that the
$$x^{2} x \frac{3}{2}(2x-1)^{-\frac{1}{2}}$$ will equal $$\frac{3x^{2}}{2\sqrt{3x-1}}$$

but i can't see how the other bit simplifies... can you show me

Thanks

 

[tiny-tim]

SORRY. Ill start a bit further back
i have this:

$$x^{2}\frac{3}{2}(2x-1)^{-1}{2} + 2x\sqrt{3x-1}$$

and I don't know how it simplifies to

$$\frac{3x^{2} + 12x^{2} - 4x}{2\sqrt{3x-1}}$$

I can't see that the
$$x^{2} x \frac{3}{2}(2x-1)^{-\frac{1}{2}}$$ will equal $$\frac{3x^{2}}{2\sqrt{3x-1}}$$

Hi thomas49th!

Do you follow:

$$\frac{3x^{2}}{2\sqrt{3x-1}}\,+\,2x\sqrt{3x-1}$$

$$= \frac{3x^{2}}{2\sqrt{3x-1}}\,+\,\frac{2x(3x-1)}{\sqrt{3x-1}}$$ ? ​

 

[thomas49th]

yes i can see a common denomitor so u multiply both the numerator and demonitor by $$2\sqrt{3x-1}$$ of the fraction
Cheerz :)