I can't identify how line 1 has simplified to line 2 in this equation. I've been staring at this for quite a while, but nothing has come to me yet. I think it's just the numerator that is confusing me, since the denominator's powers cancel nicely. I think they have divided by 3 and multiplied by something similar to $2(5x+3)^{-1}$. I just can't see what!

How did they get from line 1 to line 2?

Can anyone give me any hints? Many thanks!

  • 1
    $\begingroup$ If you expand the parentheses in the second line using the distributive law, what do you get? $\endgroup$ – Alon Amit Apr 14 '11 at 7:26
  • $\begingroup$ Ah thank you! They have taken a factor of $3(5x+3)^{-\frac{1}{2}}$ out! Right? $\endgroup$ – Danny King Apr 14 '11 at 7:29
  • $\begingroup$ Right. (filler) $\endgroup$ – Alon Amit Apr 14 '11 at 7:34

They have taken a factor of $3(5x+3)^{-\frac{1}{2}}$ out of the numerator, and simplified the denominator.

If you find yourself at a situation like line 1, think to yourself:

  • What can be simplified in the numerator and/or denominator?
  • What is common to the numerator & denominator?
  • What factors can I take out from numerator?

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