How does \sqrt{1+((x^2)/(4-x^2))} simplify to 2 times\sqrt{1/(4-x^2)}?

[Waggattack]

1.I can't figure out how the \sqrt{1+((x^2)/(4-x^2))} simplifies to 2 times\sqrt{1/(4-x^2)}


I have tried rewriting it in different ways, but I can't see how it simplifies. \sqrt{x^2 + 1/4-x^2}

 

[w3390]

The first thing to do is find a common denominator. Then you will be able to zero out some terms. Then, using the property of a square root, the square root of a fraction is the same as the square root of the numerator over the square root of the denominator. This will give you the answer.

 

[PhaseShifter]

\sqrt{1+((x^2)/(4-x^2))} simplifies to 2 times \sqrt{1/(4-x^2)}

It may help to rewrite these in a form where you don't need the parentheses.

\sqrt{1+{{x^2}\over{4-x^2}}} simplifies to 2\sqrt{{{1}\over{4-x^2}}}
Does that make it easier?

 

[njama]

Hint: 1 in the square root, 1=\frac{4-x^2}{4-x^2}

 

[HallsofIvy]

In other words, write
1+\frac{x^2}{4-x^2}
as
\frac{4- x^2}{4- x^2}+ \frac{x^2}{4- x^2}
and add the fractions.