What is (1/(x+h+2)-1/(x+2))/h ?

The solution to (1/(x+h+2)-1/(x+2))/h is -1/((x+2)(x+h+2))

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simplify (1/(x+h+2)-1/(x+2))/h

simplify

\frac{\frac{1}{x + h + 2} - \frac{1}{x + 2}}{h}

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

Solution steps

\frac{\frac{1}{x + h + 2} - \frac{1}{x + 2}}{h}

Join

\frac{1}{x + h + 2} - \frac{1}{x + 2} : - \frac{h}{( x + 2 ) ( x + h + 2 )}

= \frac{- \frac{h}{( x + 2 ) ( x + h + 2 )}}{h}

Apply the fraction rule:

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

= - \frac{\frac{h}{( x + 2 ) ( x + h + 2 )}}{h}

Apply the fraction rule:

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

\frac{\frac{h}{( x + 2 ) ( x + h + 2 )}}{h} = \frac{h}{( x + 2 ) ( x + h + 2 ) h}

= - \frac{h}{( x + 2 ) ( x + h + 2 ) h}

Cancel the common factor:

h

= - \frac{1}{( x + 2 ) ( x + h + 2 )}

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

7 x^{2} + 13 = - 14 x

x - 8 = - 5

8 x^{2} - 4 x + 21 = 0

(y + 5)^{2} = 5

What is (1/(x+h+2)-1/(x+2))/h ?
The solution to (1/(x+h+2)-1/(x+2))/h is -1/((x+2)(x+h+2))