What is 3+5/u+(2u)/(3u+1) ?

The solution to 3+5/u+(2u)/(3u+1) is (11u^2+18u+5)/(u(3u+1))

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simplify 3+5/u+(2u)/(3u+1)

simplify

3 + \frac{5}{u} + \frac{2 u}{3 u + 1}

\frac{11 u ^{2} + 18 u + 5}{u ( 3 u + 1 )}

Solution steps

3 + \frac{5}{u} + \frac{2 u}{3 u + 1}

Join

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

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

Apply the fraction rule:

a + \frac{b}{c} = \frac{a c + b}{c}

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

Simplify

3 u (3 u + 1) + 5 (3 u + 1) + 2 u^{2} : 11 u^{2} + 18 u + 5

= \frac{11 u ^{2} + 18 u + 5}{u ( 3 u + 1 )}

(7 + i) - (- 9 + i)

- - 225

\frac{3}{- \frac{2}{3}}

(4 x - 3) (3 x - 5)

(- 5^{2})^{3}

What is 3+5/u+(2u)/(3u+1) ?
The solution to 3+5/u+(2u)/(3u+1) is (11u^2+18u+5)/(u(3u+1))