# Simplify math course work

1. ### Michael_Light

117
1. The problem statement, all variables and given/known data

Simplify Please kindly show the working steps as well. ^^ Thanks.

2. Relevant equations

3. The attempt at a solution

I tried but i have no idea on how to start...

2. ### Mentallic

3,748
Re: Simplify

I can't see what you posted. Can you write it here?

3. ### Michael_Light

117
Re: Simplify

Sorry, here it goes:

4. ### Mentallic

3,748
Re: Simplify

Ok, by simplification I assume they mean rationalizing the denominator (getting rid of square roots in the denominator). Do you know about multiplying by the conjugate?

5. ### Michael_Light

117
Re: Simplify

I guess i don't know how to multiply by conjugate since i don't even know what is a conjugate. ><

6. ### Mentallic

3,748
Re: Simplify

If you have something like $$\frac{1}{1+\sqrt{x}}$$ then you can get rid of any roots in the denominator (bottom part of the fraction) by multiplying by the conjugate $$1-\sqrt{x}$$
Basically, the conjugate of a+b is a-b. When you multiply $$1+\sqrt{x}$$ by $$1-\sqrt{x}$$ you get $$1-x$$. When you multiply a-b by a+b you get $$a^2-b^2$$ so you can see that if a and b are square roots, the square roots will vanish in the denominator. So multiplying by the top and the bottom will give you $$\frac{1}{1+\sqrt{x}}=\frac{(1-\sqrt{x})}{(1+\sqrt{x})(1-\sqrt{x})}=\frac{1-\sqrt{x}}{1-x}$$
That is what you call rationalizing the denominator.

Now, for your question, the conjugate of $$\sqrt{1-x^2}+\sqrt{1+x^2}$$ will be...?

7. ### Michael_Light

117
Re: Simplify

Oo.. i don't know that is called conjugate. >< By rationalizing the denominator with its conjugate, now i managed to solve the question! Thanks! ^^