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

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

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

simplify

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

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

Solution steps

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

Apply Sum 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 ^{2} - ab + b ^{2} )}{b ^{2} - a ^{2}}

Apply Difference of Two Squares Formula:

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

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

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

Apply the commutative law:

b + a = a + b

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

Cancel the common factor:

a + b

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

3 ∣ x + 9 ∣ - 4 > 14

\frac{7}{6} + \frac{3}{5} - \frac{2}{3}

x^{2} - 10 x + 24 \geq 0

4 \leq ∣ 2 x - 8 ∣

3 k - 14 = 3 (k - 5) + 1

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