stuck?

[bobisaka]

how do i get to the final answer?




EDIT: Forgot to distribute the 4

 

[Steven G]

You should factor and not distribute. If you did not distribute the 4, then you probably would have seen that the factor of 4 in the numerator and the factor of 4 in the denominator cancels out.

 

[bobisaka]

You should factor and not distribute. If you did not distribute the 4, then you probably would have seen that the factor of 4 in the numerator and the factor of 4 in the denominator cancels out.

Okay, with that, after cancelling out the -4 in denominator and numerator, i get 4*sqr5.

I am still confused how it becomes sqr5 - 1.

 

[Steven G]

As the posting guidelines asks, please show us your work so we can see your mistake.

 

[Otis]

Hi bobisaka. I don't know why your materials instruct to distribute the factor 4 in the numerator of the product. Are you taking an online course? They also skip some steps, in their explanation; maybe they consider those prerequisites.

after cancelling out the -4 in denominator and numerator, i get 4*sqr5

Then you did not cancel the 4s correctly. Go back to the beginning of the work you'd posted, and multiply only the conjugates. Then you'll have:

(4)(1-sqrt5)/(-4)

After cancelling the factors 4, the only thing left in the numerator is (1)(1-sqrt5).

(1-sqrt5)/(-1)

Here's a hint to finish. Dividing by -1 is the same as multiplying by the reciprocal of -1, and we can write 1/(-1) as (-1)/1.

Let us know if you need more help understanding these things.

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[Otis]

Hi again. It occurred to me this morning that maybe you'd done this:

\(\displaystyle \frac{4 - 4 \sqrt{5}}{-4}\)

\(\displaystyle \frac{\cancel{4} \; \cancel{-} \; 4 \sqrt{5}}{\cancel{-} \; \cancel{4}}\)

If those improper "cancellations" look anything like what you were thinking, then let us know. We can help you find online lessons to refresh your memory on how to do arithmetic with fractions.

?

 

[HallsofIvy]

In your first post you "forgot to distribute the 4" when you wrote the incorrect "\(\displaystyle \frac{4-\sqrt{5}}{-4}\)" rather than the correct "\(\displaystyle \frac{4- 4\sqrt{5}}{-4}\)".

\(\displaystyle \frac{4- 4\sqrt{5}}{-4}= \frac{4}{-4}+ \frac{-4\sqrt{5}}{-4}\)


But when you do the division, \(\displaystyle \frac{4}{-4}= -1\), not 0 so that is \(\displaystyle -1+ \sqrt{5}\)!