What is (x^3-27y^3)/(x^2-9y^2) ?

The solution to (x^3-27y^3)/(x^2-9y^2) is (x^2+3xy+9y^2)/(x+3y)

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simplify (x^3-27y^3)/(x^2-9y^2)

simplify

\frac{x ^{3} - 27 y ^{3}}{x ^{2} - 9 y ^{2}}

\frac{x ^{2} + 3 x y + 9 y ^{2}}{x + 3 y}

Solution steps

\frac{x ^{3} - 27 y ^{3}}{x ^{2} - 9 y ^{2}}

Factor

x^{3} - 27 y^{3} : (x - 3 y) (x^{2} + 3 x y + 9 y^{2})

= \frac{( x - 3 y ) ( x ^{2} + 3 x y + 9 y ^{2} )}{x ^{2} - 9 y ^{2}}

Factor

x^{2} - 9 y^{2} : (x + 3 y) (x - 3 y)

= \frac{( x - 3 y ) ( x ^{2} + 3 x y + 9 y ^{2} )}{( x + 3 y ) ( x - 3 y )}

Cancel the common factor:

x - 3 y

= \frac{x ^{2} + 3 x y + 9 y ^{2}}{x + 3 y}

x - (- 2 x + 4)

∣ 1 - 1 ∣

\frac{10}{3} - 1

\frac{x + 4}{x ^{2} - x - 12} + \frac{2 x}{x - 4}

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

What is (x^3-27y^3)/(x^2-9y^2) ?
The solution to (x^3-27y^3)/(x^2-9y^2) is (x^2+3xy+9y^2)/(x+3y)