simplify (a^3+b^3)/(b^2-a^2) — step-by-step solution

Let's simplify:

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

We use a^3 + b^3 = (a + b)*(a^2 - a*b + b^2):

a^{3} + b^{3}

(a + b) \cdot (a^{2} - a b + b^{2})

The original denominator must remain nonzero:

a + b \neq 0

and

b - a \neq 0

We also factor the difference of squares in the denominator:

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

▶Simplified form:

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