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 )}

9 X + 7 = 52

6.7 x = 5.2 x + 12.3

x^{2} + \frac{4}{3} x + \frac{4}{9}

12 + 2 x \leq 5 (x + \frac{3}{5}) + 15

- \frac{1}{3} \leq - \frac{1}{2}

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))