What is (x^3+y^3)/(x^2-y^2) ?

The solution to (x^3+y^3)/(x^2-y^2) is (x^2-xy+y^2)/(x-y)

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simplify (x^3+y^3)/(x^2-y^2)

simplify

\frac{x ^{3} + y ^{3}}{x ^{2} - y ^{2}}

\frac{x ^{2} - x y + y ^{2}}{x - y}

Solution steps

\frac{x ^{3} + y ^{3}}{x ^{2} - y ^{2}}

Apply Sum of Cubes Formula:

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

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

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

Apply Difference of Two Squares Formula:

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

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

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

Cancel the common factor:

x + y

= \frac{x ^{2} - x y + y ^{2}}{x - y}

\frac{3}{2} x + 2 = \frac{1}{2} - \frac{1}{2} x

\frac{x ^{2} y ^{3}}{x y ^{4}}

\frac{1}{2} (x - 2) = \frac{1}{3} (x + 2)

- \frac{1}{4} + 2

a^{2} - 3 a = 10

What is (x^3+y^3)/(x^2-y^2) ?
The solution to (x^3+y^3)/(x^2-y^2) is (x^2-xy+y^2)/(x-y)