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

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

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

simplify

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

\frac{a + b}{a ^{2} + ab + b ^{2}}

Solution steps

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

Apply Difference of Two Squares Formula:

x^{2} - y^{2} = (x + y) (x - y)

a^{2} - b^{2} = (a + b) (a - b)

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

Apply Difference of Cubes Formula:

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

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

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

Cancel the common factor:

a - b

= \frac{a + b}{a ^{2} + ab + b ^{2}}

(x + 4) (2 x - 1)

(6 - 4) (- 1)

1 + 2 a - 3 a^{2} - 6 a^{3}

\frac{5 7}{35}

(8 y^{2} - 5 y + 7) - (2 y^{2} + 7 y + 11)

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