What is expand (1/(a+h)-1/a)/h ?

The solution to expand (1/(a+h)-1/a)/h is -1/(ah+a^2)

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expand (1/(a+h)-1/a)/h

expand

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

- \frac{1}{ah + a ^{2}}

Solution steps

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

Join

\frac{1}{a + h} - \frac{1}{a} : - \frac{h}{ah + a ^{2}}

= \frac{- \frac{h}{ah + a ^{2}}}{h}

Apply the fraction rule:

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

= - \frac{\frac{h}{ah + a ^{2}}}{h}

Apply the fraction rule:

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

\frac{\frac{h}{ah + a ^{2}}}{h} = \frac{h}{( ah + a ^{2} ) h}

= - \frac{h}{( ah + a ^{2} ) h}

Cancel the common factor:

h

= - \frac{1}{ah + a ^{2}}

ln (3) (x + 2)

x (x - 4)

(6 x + 4 y + 4,) (1, - 4)

1 - \frac{2}{( e - 1 ) ( e + 1 )}

\frac{d}{d t} ((x) (7 c e^{5 t} + c e^{- 3 t}))

What is expand (1/(a+h)-1/a)/h ?
The solution to expand (1/(a+h)-1/a)/h is -1/(ah+a^2)