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

The solution to 1/(3x+y)-1/(3x-y) is -(2y)/((3x+y)(3x-y))

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

simplify

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

- \frac{2 y}{( 3 x + y ) ( 3 x - y )}

Solution steps

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

Least Common Multiplier of

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

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

3 x - y - (3 x + y) : - 2 y

= \frac{- 2 y}{( 3 x + y ) ( 3 x - y )}

Apply the fraction rule:

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

= - \frac{2 y}{( 3 x + y ) ( 3 x - y )}

2 \times 2 \times 2 \times 2 \times 2 \times 2

\frac{3 5}{3 5}

16 z^{(2)} - 4

\frac{56}{7}

2 \times (- 6)

What is 1/(3x+y)-1/(3x-y) ?
The solution to 1/(3x+y)-1/(3x-y) is -(2y)/((3x+y)(3x-y))