What is expand ((n+1)/(2n+5))-(((n))/(2n+3)) ?

The solution to expand ((n+1)/(2n+5))-(((n))/(2n+3)) is 3/(4n^2+16n+15)

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expand ((n+1)/(2n+5))-(((n))/(2n+3))

expand

(\frac{n + 1}{2 n + 5}) - (\frac{( n )}{2 n + 3})

\frac{3}{4 n ^{2} + 16 n + 15}

Solution steps

(\frac{n + 1}{2 n + 5}) - (\frac{n}{2 n + 3})

Remove parentheses:

(a) = a

= \frac{n + 1}{2 n + 5} - \frac{n}{2 n + 3}

Least Common Multiplier of

2 n + 5, 2 n + 3 : (2 n + 5) (2 n + 3)

Adjust Fractions based on the LCM

= \frac{( n + 1 ) ( 2 n + 3 )}{( 2 n + 5 ) ( 2 n + 3 )} - \frac{n ( 2 n + 5 )}{( 2 n + 3 ) ( 2 n + 5 )}

Since the denominators are equal, combine the fractions:

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

= \frac{( n + 1 ) ( 2 n + 3 ) - n ( 2 n + 5 )}{( 2 n + 5 ) ( 2 n + 3 )}

Expand

(2 n + 5) (2 n + 3) : 4 n^{2} + 16 n + 15

= \frac{( n + 1 ) ( 2 n + 3 ) - n ( 2 n + 5 )}{4 n ^{2} + 16 n + 15}

Expand

(n + 1) (2 n + 3) - n (2 n + 5) : 3

= \frac{3}{4 n ^{2} + 16 n + 15}

(1 + e^{2 x})^{4}

\frac{5 ( 3 + 21 )}{6}

\frac{( 8 + x ) ( x ^{2} + x - 2 )}{2}

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

\frac{( 1 )}{( x ( x + 1 ) )}

What is expand ((n+1)/(2n+5))-(((n))/(2n+3)) ?
The solution to expand ((n+1)/(2n+5))-(((n))/(2n+3)) is 3/(4n^2+16n+15)