What is ((x^8+2x^7-3x^6+2x^5-x^4))/((x^4)) ?

The solution to ((x^8+2x^7-3x^6+2x^5-x^4))/((x^4)) is x^4+2x^3-3x^2+2x-1

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simplify ((x^8+2x^7-3x^6+2x^5-x^4))/((x^4))

simplify

\frac{( x ^{8} + 2 x ^{7} - 3 x ^{6} + 2 x ^{5} - x ^{4} )}{( x ^{4} )}

x^{4} + 2 x^{3} - 3 x^{2} + 2 x - 1

Solution steps

\frac{x ^{8} + 2 x ^{7} - 3 x ^{6} + 2 x ^{5} - x ^{4}}{x ^{4}}

Factor

x^{8} + 2 x^{7} - 3 x^{6} + 2 x^{5} - x^{4} : x^{4} (x^{4} + 2 x^{3} - 3 x^{2} + 2 x - 1)

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

Cancel the common factor:

x^{4}

= x^{4} + 2 x^{3} - 3 x^{2} + 2 x - 1

\frac{7 - y}{y - 7}

\frac{x ^{2} - 25}{5 - x}

- 2 7^{\frac{4}{3}}

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

(2 x - 2) (3 x + 5)

What is ((x^8+2x^7-3x^6+2x^5-x^4))/((x^4)) ?
The solution to ((x^8+2x^7-3x^6+2x^5-x^4))/((x^4)) is x^4+2x^3-3x^2+2x-1