What is 1/(x+y+3)-1/(x+3) ?

The solution to 1/(x+y+3)-1/(x+3) is -y/((x+3)(x+y+3))

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simplify 1/(x+y+3)-1/(x+3)

simplify

\frac{1}{x + y + 3} - \frac{1}{x + 3}

- \frac{y}{( x + 3 ) ( x + y + 3 )}

Solution steps

\frac{1}{x + y + 3} - \frac{1}{x + 3}

Least Common Multiplier of

x + y + 3, x + 3 : (x + 3) (x + y + 3)

Adjust Fractions based on the LCM

= \frac{x + 3}{( x + 3 ) ( x + y + 3 )} - \frac{x + y + 3}{( x + 3 ) ( x + y + 3 )}

Apply the fraction rule:

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

= \frac{x + 3 - ( x + y + 3 )}{( x + 3 ) ( x + y + 3 )}

Simplify

x + 3 - (x + y + 3) : - y

= \frac{- y}{( x + 3 ) ( x + y + 3 )}

Apply the fraction rule:

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

= - \frac{y}{( x + 3 ) ( x + y + 3 )}

\frac{1}{3} \cdot x

[(- 2)^{2}]^{4}

0 + (- 6)

\frac{sin ^{3} ( x )}{cos ( x )}

(\frac{5}{7} - \frac{3}{14})^{4}

What is 1/(x+y+3)-1/(x+3) ?
The solution to 1/(x+y+3)-1/(x+3) is -y/((x+3)(x+y+3))