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

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

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

simplify

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

x^{2} + y^{2} + 1 + 1

Solution steps

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

Multiply by the conjugate

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

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

(x^{2} + y^{2} + 1 - 1) (x^{2} + y^{2} + 1 + 1) = x^{2} + y^{2}

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

Cancel the common factor:

x^{2} + y^{2}

= x^{2} + y^{2} + 1 + 1

\frac{m ^{2} - 2 m + 1}{m - 1}

\frac{11}{30}

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

x \cdot (x + 1)

4 x^{2} + 20 x

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