What is (xsqrt(x^2+36)*3-2(x^2+36))/(6(x^2+36)) ?

The solution to (xsqrt(x^2+36)*3-2(x^2+36))/(6(x^2+36)) is (3x-2sqrt(x^2+36))/(6sqrt(x^2+36))

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simplify (xsqrt(x^2+36)*3-2(x^2+36))/(6(x^2+36))

simplify

\frac{x x ^{2} + 36 \cdot 3 - 2 ( x ^{2} + 36 )}{6 ( x ^{2} + 36 )}

\frac{3 x - 2 x ^{2} + 36}{6 x ^{2} + 36}

Solution steps

\frac{x x ^{2} + 36 \cdot 3 - 2 ( x ^{2} + 36 )}{6 ( x ^{2} + 36 )}

Factor out common term

x^{2} + 36 : x^{2} + 36 (x \cdot 3 - 2 x^{2} + 36)

= \frac{x ^{2} + 36 ( x \cdot 3 - 2 x ^{2} + 36 )}{6 ( x ^{2} + 36 )}

Apply radical rule:

a = a a

x^{2} + 36 = x^{2} + 36 x^{2} + 36

= \frac{x ^{2} + 36 ( x \cdot 3 - 2 x ^{2} + 36 )}{6 x ^{2} + 36 x ^{2} + 36}

Cancel the common factor:

x^{2} + 36

= \frac{x \cdot 3 - 2 x ^{2} + 36}{6 x ^{2} + 36}

= \frac{3 x - 2 x ^{2} + 36}{6 x ^{2} + 36}

ln (4) m^{3} n^{5}

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

\frac{u ^{5} ( u ^{3} + 1 )}{u ^{2} + 1}

- \frac{1 ( 3 + 6 - 8 + 3 )}{- 1 ( 3 + 6 - 8 + 3 )}

\frac{d}{d v} ((p) (p + \frac{1.9}{v ^{2}}) (v - 7, 2))

What is (xsqrt(x^2+36)*3-2(x^2+36))/(6(x^2+36)) ?
The solution to (xsqrt(x^2+36)*3-2(x^2+36))/(6(x^2+36)) is (3x-2sqrt(x^2+36))/(6sqrt(x^2+36))