What is ((x^3-4x^2+x+6))/((x^2-2x-3)) ?

The solution to ((x^3-4x^2+x+6))/((x^2-2x-3)) is x-2

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simplify ((x^3-4x^2+x+6))/((x^2-2x-3))

simplify

\frac{( x ^{3} - 4 x ^{2} + x + 6 )}{( x ^{2} - 2 x - 3 )}

x - 2

Solution steps

\frac{x ^{3} - 4 x ^{2} + x + 6}{x ^{2} - 2 x - 3}

Factor

x^{3} - 4 x^{2} + x + 6 : (x + 1) (x - 2) (x - 3)

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

Factor

x^{2} - 2 x - 3 : (x + 1) (x - 3)

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

Cancel the common factor:

x + 1

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

Cancel the common factor:

x - 3

= x - 2

(x + 2 y) (x + 2 y + 4) - 12

50 x^{2} + 18 y^{2}

\frac{( 3 x ^{2} + 16 x + 5 )}{( 9 x ^{2} - 1 )}

(2 n + 1)^{5}

(5 x^{2} y + 2 x)^{3}

What is ((x^3-4x^2+x+6))/((x^2-2x-3)) ?
The solution to ((x^3-4x^2+x+6))/((x^2-2x-3)) is x-2