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

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

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

simplify

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

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

Solution steps

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

Least Common Multiplier of

a + h, a : a (h + a)

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

a - (h + a) : - h

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

Apply the fraction rule:

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

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

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