What is 9/(x+h)-9/x ?

The solution to 9/(x+h)-9/x is -(9h)/(x(x+h))

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simplify 9/(x+h)-9/x

simplify

\frac{9}{x + h} - \frac{9}{x}

- \frac{9 h}{x ( x + h )}

Solution steps

\frac{9}{x + h} - \frac{9}{x}

Least Common Multiplier of

x + h, x : x (x + h)

Adjust Fractions based on the LCM

= \frac{9 x}{x ( x + h )} - \frac{9 ( x + h )}{x ( x + h )}

Apply the fraction rule:

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

= \frac{9 x - 9 ( x + h )}{x ( x + h )}

Simplify

9 x - 9 (x + h) : - 9 h

= \frac{- 9 h}{x ( x + h )}

Apply the fraction rule:

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

= - \frac{9 h}{x ( x + h )}

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