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

The solution to sqrt(1/(x^2+4)+1) is sqrt((x^2+5)/(x^2+4))

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

simplify

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

\frac{x ^{2} + 5}{x ^{2} + 4}

Solution steps

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

Apply the fraction rule:

1 + \frac{b}{c} = \frac{c + b}{c}

= \frac{( x ^{2} + 4 ) + 1}{x ^{2} + 4}

Simplify

(x^{2} + 4) + 1 : x^{2} + 5

= \frac{x ^{2} + 5}{x ^{2} + 4}

\frac{21}{4}

\frac{5}{6} \cdot 9

3 y^{2} - y - 2

\frac{x ^{2}}{y ^{2}} - 1

\frac{- 8}{2}

What is sqrt(1/(x^2+4)+1) ?
The solution to sqrt(1/(x^2+4)+1) is sqrt((x^2+5)/(x^2+4))