What is (5x^4-9x^3-23x^2+36x+12)/(x^2-4) ?

The solution to (5x^4-9x^3-23x^2+36x+12)/(x^2-4) is 5x^2-9x-3

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simplify (5x^4-9x^3-23x^2+36x+12)/(x^2-4)

simplify

\frac{5 x ^{4} - 9 x ^{3} - 23 x ^{2} + 36 x + 12}{x ^{2} - 4}

5 x^{2} - 9 x - 3

Solution steps

\frac{5 x ^{4} - 9 x ^{3} - 23 x ^{2} + 36 x + 12}{x ^{2} - 4}

Factor

5 x^{4} - 9 x^{3} - 23 x^{2} + 36 x + 12 : (x - 2) (x + 2) (5 x^{2} - 9 x - 3)

= \frac{( x - 2 ) ( x + 2 ) ( 5 x ^{2} - 9 x - 3 )}{x ^{2} - 4}

Factor

x^{2} - 4 : (x + 2) (x - 2)

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

Cancel the common factor:

x - 2

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

Cancel the common factor:

x + 2

= 5 x^{2} - 9 x - 3

1 2^{8}

\frac{9}{7 + 2}

(3 + 1) (3 + 2)

\frac{5 r - 5 3 r}{5 - 3 3 r ^{2}}

(8 + 11) (8 - 11)

What is (5x^4-9x^3-23x^2+36x+12)/(x^2-4) ?
The solution to (5x^4-9x^3-23x^2+36x+12)/(x^2-4) is 5x^2-9x-3