What is (a^2+b^2)/(a^3+b^3)-1/(a+b) ?

The solution to (a^2+b^2)/(a^3+b^3)-1/(a+b) is (ab)/(a^3+b^3)

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simplify (a^2+b^2)/(a^3+b^3)-1/(a+b)

simplify

\frac{a ^{2} + b ^{2}}{a ^{3} + b ^{3}} - \frac{1}{a + b}

\frac{ab}{a ^{3} + b ^{3}}

Solution steps

\frac{a ^{2} + b ^{2}}{a ^{3} + b ^{3}} - \frac{1}{a + b}

Least Common Multiplier of

a^{3} + b^{3}, a + b : (a + b) (a^{3} + b^{3})

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

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

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

Cancel

\frac{a ^{2} b + a b ^{2}}{( a + b ) ( a ^{3} + b ^{3} )} : \frac{ab}{a ^{3} + b ^{3}}

= \frac{ab}{a ^{3} + b ^{3}}

x^{3} + 3 x^{2} - 5 x - 15

- 10 + 8 m = - 2 (7 m - 3) + 6

x^{2} - 13 x y - 30 y^{2}

- \frac{3}{2} \cdot 6

n + 6 \leq 8

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