What is sqrt(1+(x^2)/(4-x^2)) ?

The solution to sqrt(1+(x^2)/(4-x^2)) is (2sqrt(4-x^2))/(4-x^2)

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simplify sqrt(1+(x^2)/(4-x^2))

simplify

1 + \frac{x ^{2}}{4 - x ^{2}}

\frac{2 4 - x ^{2}}{4 - x ^{2}}

Solution steps

1 + \frac{x ^{2}}{4 - x ^{2}}

Join

1 + \frac{x ^{2}}{4 - x ^{2}} : \frac{4}{4 - x ^{2}}

= \frac{4}{4 - x ^{2}}

Apply radical rule:

assuming

a \geq 0, b \geq 0

= \frac{4}{4 - x ^{2}}

4 = 2

= \frac{2}{4 - x ^{2}}

Rationalize

\frac{2}{4 - x ^{2}} : \frac{2 - x ^{2} + 4}{- x ^{2} + 4}

= \frac{2 - x ^{2} + 4}{4 - x ^{2}}

\frac{7 - 6 i}{7 + i}

lo g_{8} (- 1)

\frac{5 + 5 i}{1 + i}

- 2 - 16

- 30 \div 10

What is sqrt(1+(x^2)/(4-x^2)) ?
The solution to sqrt(1+(x^2)/(4-x^2)) is (2sqrt(4-x^2))/(4-x^2)