What is (x^5+y^5)/(x+y) ?

The solution to (x^5+y^5)/(x+y) is x^4-x^3y+x^2y^2-xy^3+y^4

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simplify (x^5+y^5)/(x+y)

simplify

\frac{x ^{5} + y ^{5}}{x + y}

x^{4} - x^{3} y + x^{2} y^{2} - x y^{3} + y^{4}

Solution steps

\frac{x ^{5} + y ^{5}}{x + y}

Apply factoring rule:

x^{n} + y^{n} = (x + y) (x^{n - 1} - x^{n - 2} y + \dots - x y^{n - 2} + y^{n - 1}), n i s o dd

x^{5} + y^{5} = (x + y) (x^{4} - x^{3} y + x^{2} y^{2} - x y^{3} + y^{4})

= \frac{( x + y ) ( x ^{4} - x ^{3} y + x ^{2} y ^{2} - x y ^{3} + y ^{4} )}{x + y}

Cancel the common factor:

x + y

= x^{4} - x^{3} y + x^{2} y^{2} - x y^{3} + y^{4}

90 - 610

(- 2 y)^{2}

(x^{2} + 4)^{3}

ln (x^{7})

x^{2} - 2^{2}

What is (x^5+y^5)/(x+y) ?
The solution to (x^5+y^5)/(x+y) is x^4-x^3y+x^2y^2-xy^3+y^4