# Silly me: Not thinking straight today: simple questions

• mike_302
In summary, the first equation says that y^2 + 1 is the same as 1 if the same equation is divided by itself. The second equation just factors the top and you should see the answer.

## Homework Statement

Two equations here, I need to simplify both of them but I'm not too sure:
(y^2+1)/(y^2+1) as well as (t^2-s^2)/(s+t)^2

## The Attempt at a Solution

If you typed in the first one correctly then it should just simplify to 1 if the same equation divided by itself. The second one just factor the top and you should see the answer.

I hope you take a look at the first one again, if you typed it right. It looks like

$$\frac{y^2 + 1}{y^2 + 1}$$

For the second one, think how you would factor the numerator. Is it special in any way?

Oops, sorry, first one is y^2+1/y^2-1 ... But I don't quite get what You mean on the second one. Sorry, I realize these are probably cereal box games to you but today is not my day for thinking... I've been out of it.

I got the second one to: t^2-s^2 / t^2+s^2 ... But the back of the book says its going to be t-s/t+s ...

For the first question, it says you cannot simplify further than what it's already at.

I do not know of any simple way to simplify

$$\frac{y^2 + 1}{y^2 - 1}$$

For your other problem however, don't run away from it. We are telling you that there is a way to factor the numerator. It is a common factorization that you need to get used to, so look again in your book or your study aid or try to think about an answer.

EDIT: Yes, the book is right; there isn't anyway to simplify the first one. That's because all the simplifications you are doing rely on factorization and then canceling factors in the resulting fraction. There is no way to factor $y^2 + 1$ and have it cancel out with a factor of $y^2 - 1$. However, it is possible to factor $t^2 - s^2$. Figure out how, and you will have solved your problem.

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(s+t)^2 is not t^2+s^2 remember the that (s+t)^2 is (s+t)(s+t), but if you factor the top you do not have to expand the bottom.

OHH! I see how to factor the top. -1(s^2+t^2) . then... then it just equals -1?

EDIT: Wait, No, I see the error in that... Still not getting is :S

I think what's confusing me is knowing that the answer has to have both the exponents come out of the equation, and I don't see how they do that without dividing the top and bottom which... you can't do.

Try multiplying (a - b) with (a + b)

see, that solved it. Thanks. I was doing (a-b)^2 = (a-b)(a-b)

## What causes us to have "off" days where we make simple mistakes?

There are a number of potential factors that can contribute to feeling like we are not thinking straight. These can include stress, lack of sleep, nutritional deficiency, illness, or simply being distracted or preoccupied with other things.

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Sometimes it can be helpful to take a break and clear our minds before tackling a task that requires focus and attention. Additionally, practicing mindfulness and being present in the moment can help prevent our minds from wandering and making mistakes.

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If you are consistently experiencing difficulty with cognitive tasks or if these "off" days are significantly impacting your daily life, it may be a good idea to consult with a healthcare professional to rule out any underlying medical conditions.