How do you solve this limit? I already attempted to, but I know I had to have gone wrong somewhere because I keep getting the wrong answer. I tried multiplying by the conjugate, but I keep thinking the limit will not exist.

Question

anonymous · Answer

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anonymous · Answer

why doesn't multiplying by the conjugate work? 
i can show you another method if you like, but that should work as well

anonymous · Answer

I think I just did something wrong in the process of multiplying by the conjugate. If I show you my work, could you tell me where I went wrong?

anonymous · Answer

sure

anonymous · Answer

try multiplying again by the conjugate

anonymous · Answer

then i will show you method number 2

anonymous · Answer

Were you able to get it?

anonymous · Answer

attachment

anonymous · Answer

leave the numerator in factored form
don't multiply out
then you can cancel the $1-x$ top and bottom

anonymous · Answer

$$\frac{(1-x)(1+\sqrt{x})}{1-x}$$ is what you want to look at
do  not multiply in the numerator 
cancel

anonymous · Answer

Oh my gosh. I can't believe I made such a stupid mistake XD Just, wow. Thanks! I knew I had to have made a silly mistake somewhere in there.

anonymous · Answer

allow me to show you method 2
factor the numerator as 
$$1-x=(1+\sqrt{x})(1-\sqrt{x})$$ then cancel

anonymous · Answer

Ahh. That makes sense. Awesome- I'll use that for this next problem I'm working on. Thanks!

anonymous · Answer

yw