What is (4-x^2)/(3-sqrt(x^2+5)) ?

The solution to (4-x^2)/(3-sqrt(x^2+5)) is 3+sqrt(x^2+5)

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simplify (4-x^2)/(3-sqrt(x^2+5))

simplify

\frac{4 - x ^{2}}{3 - x ^{2} + 5}

3 + x^{2} + 5

Solution steps

\frac{4 - x ^{2}}{3 - x ^{2} + 5}

Multiply by the conjugate

\frac{3 + x ^{2} + 5}{3 + x ^{2} + 5}

= \frac{( 4 - x ^{2} ) ( 3 + x ^{2} + 5 )}{( 3 - x ^{2} + 5 ) ( 3 + x ^{2} + 5 )}

(3 - x^{2} + 5) (3 + x^{2} + 5) = - x^{2} + 4

= \frac{( 4 - x ^{2} ) ( 3 + x ^{2} + 5 )}{- x ^{2} + 4}

Cancel the common factor:

4 - x^{2}

= 3 + x^{2} + 5

\frac{1 - i}{4 - 3 i}

- 4 - 36

0. 1^{7}

\frac{16}{64}

(5 ab)^{\frac{3}{2}}

What is (4-x^2)/(3-sqrt(x^2+5)) ?
The solution to (4-x^2)/(3-sqrt(x^2+5)) is 3+sqrt(x^2+5)