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

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

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

simplify

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

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

Solution steps

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

Least Common Multiplier of

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

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

x + 2 - (x + h + 2) : - h

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

Apply the fraction rule:

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

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

5 a + 2 a

2 \frac{1}{2} \cdot \frac{1}{3}

\frac{7 3}{3}

\frac{5 ^{- 6}}{5 ^{3}}

\frac{4 x - 6}{2 3 x}

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