What is (sqrt(x-5))/(sqrt(x-5)+\sqrt{x+5)} ?

The solution to (sqrt(x-5))/(sqrt(x-5)+\sqrt{x+5)} is -((sqrt(x-5)-sqrt(x+5))sqrt(x-5))/(10)

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simplify (sqrt(x-5))/(sqrt(x-5)+\sqrt{x+5)}

simplify

\frac{x - 5}{x - 5 + x + 5}

- \frac{( x - 5 - x + 5 ) x - 5}{10}

Solution steps

\frac{x - 5}{x - 5 + x + 5}

Multiply by the conjugate

\frac{x - 5 - x + 5}{x - 5 - x + 5}

= \frac{x - 5 ( x - 5 - x + 5 )}{( x - 5 + x + 5 ) ( x - 5 - x + 5 )}

(x - 5 + x + 5) (x - 5 - x + 5) = - 10

= \frac{( x - 5 - x + 5 ) x - 5}{- 10}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{( x - 5 - x + 5 ) x - 5}{10}

\frac{- 2 + - 4}{2}

\frac{20}{5 7 - 2 5}

\frac{2 ^{3}}{2 ^{6}}

+ 49 r^{2} - 64

5 x 4^{3}

What is (sqrt(x-5))/(sqrt(x-5)+\sqrt{x+5)} ?
The solution to (sqrt(x-5))/(sqrt(x-5)+\sqrt{x+5)} is -((sqrt(x-5)-sqrt(x+5))sqrt(x-5))/(10)