What is ((sqrt(p+q)+sqrt(p-q))^2)/(2q) ?

The solution to ((sqrt(p+q)+sqrt(p-q))^2)/(2q) is (p+sqrt(p+q)sqrt(p-q))/q

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simplify ((sqrt(p+q)+sqrt(p-q))^2)/(2q)

simplify

\frac{( p + q + p - q ) ^{2}}{2 q}

\frac{p + p + q p - q}{q}

Solution steps

\frac{( p + q + p - q ) ^{2}}{2 q}

Expand

(p + q + p - q)^{2} : 2 p + 2 p + q p - q

= \frac{2 p + 2 p + q p - q}{2 q}

Factor out common term

2

= \frac{2 ( p + p + q p - q )}{2 q}

Cancel the common factor:

2

= \frac{p + p + q p - q}{q}

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\frac{1}{( 3 n + 1 ) ^{15}}

(2 - 1 - 4 x^{2})^{2}

What is ((sqrt(p+q)+sqrt(p-q))^2)/(2q) ?
The solution to ((sqrt(p+q)+sqrt(p-q))^2)/(2q) is (p+sqrt(p+q)sqrt(p-q))/q