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

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

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

simplify

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

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

Solution steps

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

Least Common Multiplier of

2 (x + h), 2 x : 2 x (x + h)

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

x - (x + h) : - h

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

Apply the fraction rule:

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

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

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\frac{1}{sin ( x ) \cdot cos ( x )}