What is (2x+10)/(sqrt(x+7)-\sqrt{2)} ?

The solution to (2x+10)/(sqrt(x+7)-\sqrt{2)} is 2(sqrt(x+7)+sqrt(2))

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simplify (2x+10)/(sqrt(x+7)-\sqrt{2)}

simplify

\frac{2 x + 10}{x + 7 - 2}

2 (x + 7 + 2)

Solution steps

\frac{2 x + 10}{x + 7 - 2}

Multiply by the conjugate

\frac{x + 7 + 2}{x + 7 + 2}

= \frac{( 2 x + 10 ) ( x + 7 + 2 )}{( x + 7 - 2 ) ( x + 7 + 2 )}

(x + 7 - 2) (x + 7 + 2) = x + 5

= \frac{( 2 x + 10 ) ( x + 7 + 2 )}{x + 5}

Factor

2 x + 10 : 2 (x + 5)

= \frac{2 ( x + 5 ) ( x + 7 + 2 )}{x + 5}

Cancel the common factor:

x + 5

= 2 (x + 7 + 2)

(5 x + 7)^{8}

- 43

- 2 x \cdot (- x)

(9 x - 4) (9 x + 4)

\frac{6 y ^{3}}{2 x ^{- 2} y ^{3}}

What is (2x+10)/(sqrt(x+7)-\sqrt{2)} ?
The solution to (2x+10)/(sqrt(x+7)-\sqrt{2)} is 2(sqrt(x+7)+sqrt(2))