What is ((1/(1+x+h)-1/(1+x)))/h ?

The solution to ((1/(1+x+h)-1/(1+x)))/h is -1/((x+1)(x+h+1))

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simplify ((1/(1+x+h)-1/(1+x)))/h

simplify

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

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

Solution steps

\frac{\frac{1}{1 + x + h} - \frac{1}{1 + x}}{h}

Join

\frac{1}{1 + x + h} - \frac{1}{1 + x} : - \frac{h}{( x + 1 ) ( x + h + 1 )}

= \frac{- \frac{h}{( x + 1 ) ( x + h + 1 )}}{h}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{\frac{h}{( x + 1 ) ( x + h + 1 )}}{h}

Apply the fraction rule:

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

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

= - \frac{h}{( x + 1 ) ( x + h + 1 ) h}

Cancel the common factor:

h

= - \frac{1}{( x + 1 ) ( x + h + 1 )}

10 - 4 ∣ 2 - 4 x ∣ = - 2

k^{2} - k + 11 = 11

- 2 (2)^{2}

\frac{2}{3}

\frac{3}{8} + \frac{5}{8} + \frac{2}{8}

What is ((1/(1+x+h)-1/(1+x)))/h ?
The solution to ((1/(1+x+h)-1/(1+x)))/h is -1/((x+1)(x+h+1))