Simplify math course work

Michael_Light

Homework Statement

Simplify [PLAIN]http://www4c.wolframalpha.com/Calculate/MSP/MSP249819e8ec729ig8433b00002e0fh793haeag630?MSPStoreType=image/gif&s=15&w=137&h=59 [Broken] Please kindly show the working steps as well. ^^ Thanks.

The Attempt at a Solution

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

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Homework Helper

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

Homework Helper

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?

Michael_Light

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?

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

Homework Helper

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...?

Michael_Light

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...?

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