What is (x^6+6x^3-2x^5-7x^2-4x+6)/(x^4-3x^2+2) ?

The solution to (x^6+6x^3-2x^5-7x^2-4x+6)/(x^4-3x^2+2) is (x^4-2x^3+x^2+4x-6)/(x^2-2)

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simplify (x^6+6x^3-2x^5-7x^2-4x+6)/(x^4-3x^2+2)

simplify

\frac{x ^{6} + 6 x ^{3} - 2 x ^{5} - 7 x ^{2} - 4 x + 6}{x ^{4} - 3 x ^{2} + 2}

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

Solution steps

\frac{x ^{6} + 6 x ^{3} - 2 x ^{5} - 7 x ^{2} - 4 x + 6}{x ^{4} - 3 x ^{2} + 2}

Factor

x^{6} + 6 x^{3} - 2 x^{5} - 7 x^{2} - 4 x + 6 : (x - 1) (x + 1) (x^{4} - 2 x^{3} + x^{2} + 4 x - 6)

= \frac{( x - 1 ) ( x + 1 ) ( x ^{4} - 2 x ^{3} + x ^{2} + 4 x - 6 )}{x ^{4} - 3 x ^{2} + 2}

Factor

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

= \frac{( x - 1 ) ( x + 1 ) ( x ^{4} - 2 x ^{3} + x ^{2} + 4 x - 6 )}{( x + 1 ) ( x - 1 ) ( x ^{2} - 2 )}

Cancel the common factor:

x - 1

= \frac{( x + 1 ) ( x ^{4} - 2 x ^{3} + x ^{2} + 4 x - 6 )}{( x + 1 ) ( x ^{2} - 2 )}

Cancel the common factor:

x + 1

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

- 5 \times (- 5)

(7 + i) - (6 - 4 i)

(5 x + 3) (5 x - 3)

\frac{\frac{x - 5}{x - 4}}{\frac{x - 12}{x - 4}}

a x + b x

What is (x^6+6x^3-2x^5-7x^2-4x+6)/(x^4-3x^2+2) ?
The solution to (x^6+6x^3-2x^5-7x^2-4x+6)/(x^4-3x^2+2) is (x^4-2x^3+x^2+4x-6)/(x^2-2)