What is expand 1/((x-a)^3)-1/((x+a)^3) ?

The solution to expand 1/((x-a)^3)-1/((x+a)^3) is (6ax^2+2a^3)/(x^6-3a^2x^4+3a^4x^2-a^6)

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expand 1/((x-a)^3)-1/((x+a)^3)

expand

\frac{1}{( x - a ) ^{3}} - \frac{1}{( x + a ) ^{3}}

\frac{6 a x ^{2} + 2 a ^{3}}{x ^{6} - 3 a ^{2} x ^{4} + 3 a ^{4} x ^{2} - a ^{6}}

Solution steps

\frac{1}{( x - a ) ^{3}} - \frac{1}{( x + a ) ^{3}}

(x - a)^{3} = x^{3} - 3 a x^{2} + 3 a^{2} x - a^{3}

= \frac{1}{x ^{3} - 3 a x ^{2} + 3 a ^{2} x - a ^{3}} - \frac{1}{( x + a ) ^{3}}

(x + a)^{3} = x^{3} + 3 a x^{2} + 3 a^{2} x + a^{3}

= \frac{1}{x ^{3} - 3 a x ^{2} + 3 a ^{2} x - a ^{3}} - \frac{1}{x ^{3} + 3 a x ^{2} + 3 a ^{2} x + a ^{3}}

Factor

x^{3} - 3 x^{2} a + 3 x a^{2} - a^{3} : (x - a)^{3}

= \frac{1}{( x - a ) ^{3}} - \frac{1}{x ^{3} + 3 x ^{2} a + 3 x a ^{2} + a ^{3}}

Factor

x^{3} + 3 x^{2} a + 3 x a^{2} + a^{3} : (x + a)^{3}

= \frac{1}{( x - a ) ^{3}} - \frac{1}{( x + a ) ^{3}}

Least Common Multiplier of

(x - a)^{3}, (x + a)^{3} : (x - a)^{3} (x + a)^{3}

Adjust Fractions based on the LCM

= \frac{( x + a ) ^{3}}{( x - a ) ^{3} ( x + a ) ^{3}} - \frac{( x - a ) ^{3}}{( x - a ) ^{3} ( x + a ) ^{3}}

Since the denominators are equal, combine the fractions:

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

= \frac{( x + a ) ^{3} - ( x - a ) ^{3}}{( x - a ) ^{3} ( x + a ) ^{3}}

(x - a)^{3} = x^{3} - 3 a x^{2} + 3 a^{2} x - a^{3}

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

(x + a)^{3} = x^{3} + 3 a x^{2} + 3 a^{2} x + a^{3}

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

Expand

(x^{3} - 3 x^{2} a + 3 x a^{2} - a^{3}) (x^{3} + 3 x^{2} a + 3 x a^{2} + a^{3}) : x^{6} - 3 a^{2} x^{4} + 3 a^{4} x^{2} - a^{6}

= \frac{( x + a ) ^{3} - ( x - a ) ^{3}}{x ^{6} - 3 a ^{2} x ^{4} + 3 a ^{4} x ^{2} - a ^{6}}

Expand

(x + a)^{3} - (x - a)^{3} : 6 a x^{2} + 2 a^{3}

= \frac{6 a x ^{2} + 2 a ^{3}}{x ^{6} - 3 a ^{2} x ^{4} + 3 a ^{4} x ^{2} - a ^{6}}

\frac{( 400 - x ) ^{2}}{100}

x^{x^{x}} (x^{x} ln (x) (ln (x) + 1) + (x^{x - 1}))

o f (o, x, y) (x^{2} + 2 y^{2} = 4)

\frac{d}{d x} ((10 x + 8) e^{x^{2}}) + cos (x)

40 (1 - e^{- 2 t} - 2 e t^{- 2 t})

What is expand 1/((x-a)^3)-1/((x+a)^3) ?
The solution to expand 1/((x-a)^3)-1/((x+a)^3) is (6ax^2+2a^3)/(x^6-3a^2x^4+3a^4x^2-a^6)