Hello!
I would really appreciate some help, I need to simplify these;
x + √x
------- (I know that this one is √x, but how does it get to that?)
1 + √x
and;
x
------- + √(1-x)
√(1-x)
and;
1 - x
-------
1 + √x
Thank you!
factor out $\displaystyle \sqrt{x}$ from the numerator:
we get: $\displaystyle \frac {\sqrt{x} (\sqrt{x} + 1)}{1 + \sqrt{x}}$
now continue
begin by combining the fractions. then what would you get?
and;
x
------- + √(1-x)
√(1-x)
think of $\displaystyle 1 - x$ as $\displaystyle 1^2 - (\sqrt{x})^2$and;
1 - x
-------
1 + √x
Thank you!
now expand that using the difference of two squares. what do you get?