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

The solution to factor 1/((x-a)^3)-1/((x+a)^3) is (2a(3x^2+a^2))/((x-a)^3(x+a)^3)

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

factor

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

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

Solution steps

\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}}

Expand

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

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

Factor

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

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

lo g_{3} (3.3)

8^{3} - 9 \cdot 2 \div 3

- 9 - (- 4)

8 x^{2} + 18 x + 9 = 0

3 x^{2} - 12 x + 10 = 0

What is factor 1/((x-a)^3)-1/((x+a)^3) ?
The solution to factor 1/((x-a)^3)-1/((x+a)^3) is (2a(3x^2+a^2))/((x-a)^3(x+a)^3)