What is (sqrt(7)-sqrt(5))/(sqrt(7)+\sqrt{5)} ?

The solution to (sqrt(7)-sqrt(5))/(sqrt(7)+\sqrt{5)} is 6-sqrt(35)

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simplify (sqrt(7)-sqrt(5))/(sqrt(7)+\sqrt{5)}

simplify

\frac{7 - 5}{7 + 5}

6 - 35

Decimal Notation

0.08392 \dots

Solution steps

\frac{7 - 5}{7 + 5}

Multiply by the conjugate

\frac{7 - 5}{7 - 5}

= \frac{( 7 - 5 ) ( 7 - 5 )}{( 7 + 5 ) ( 7 - 5 )}

Expand

(7 - 5) (7 - 5) : 12 - 235

Expand

(7 + 5) (7 - 5) : 2

= \frac{12 - 2 35}{2}

Factor out common term

2 : 2 (6 - 35)

= \frac{2 ( 6 - 35 )}{2}

Cancel the common factor:

2

= 6 - 35

(x^{2} + 2 y)^{2}

\frac{- 2 x ^{3} + 4 x}{- 6 x + \frac{1}{x}} (- 1)

\frac{1}{5} \cdot \frac{4}{5}

2 x^{2} + 2 x - 6

\frac{4 x ^{3} y ^{5}}{12 x ^{4} y ^{3}}

What is (sqrt(7)-sqrt(5))/(sqrt(7)+\sqrt{5)} ?
The solution to (sqrt(7)-sqrt(5))/(sqrt(7)+\sqrt{5)} is 6-sqrt(35)