What is k/(2k+1)+1/((2k+1)(2k+3)) ?

The solution to k/(2k+1)+1/((2k+1)(2k+3)) is (k+1)/(2k+3)

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simplify k/(2k+1)+1/((2k+1)(2k+3))

simplify

\frac{k}{2 k + 1} + \frac{1}{( 2 k + 1 ) ( 2 k + 3 )}

\frac{k + 1}{2 k + 3}

Solution steps

\frac{k}{2 k + 1} + \frac{1}{( 2 k + 1 ) ( 2 k + 3 )}

Least Common Multiplier of

2 k + 1, (2 k + 1) (2 k + 3) : (2 k + 1) (2 k + 3)

Adjust Fractions based on the LCM

= \frac{k ( 2 k + 3 )}{( 2 k + 1 ) ( 2 k + 3 )} + \frac{1}{( 2 k + 1 ) ( 2 k + 3 )}

Apply the fraction rule:

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

= \frac{k ( 2 k + 3 ) + 1}{( 2 k + 1 ) ( 2 k + 3 )}

Simplify

k (2 k + 3) + 1 : 2 k^{2} + 3 k + 1

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

Cancel

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

= \frac{k + 1}{2 k + 3}

3 x^{2} - 2 x (x - 4) = x - 12

8 x - 48 = 6 x + 32

0. 9^{3}

\frac{2 π}{\frac{π}{5}}

337 5^{\frac{1}{3}}

What is k/(2k+1)+1/((2k+1)(2k+3)) ?
The solution to k/(2k+1)+1/((2k+1)(2k+3)) is (k+1)/(2k+3)