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

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

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

simplify

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

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

Solution steps

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

Join

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

= \frac{- \frac{h}{a ( h + a )}}{h}

Apply the fraction rule:

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

= - \frac{\frac{h}{a ( h + a )}}{h}

Apply the fraction rule:

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

\frac{\frac{h}{a ( h + a )}}{h} = \frac{h}{a ( h + a ) h}

= - \frac{h}{a ( h + a ) h}

Cancel the common factor:

h

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

21 \div 7

2 (x + y)

(2 - i) - (- 4 + 8 i)

g (- 3)

\frac{cos ( x )}{1 - tan ( x )} + \frac{sin ( x )}{1 - cot ( x )}