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

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

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

simplify

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

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

Solution steps

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

Factor

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

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

Factor

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

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

Cancel the common factor:

(x - 1)^{2}

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

(x - 1) (x + 9)

\frac{22}{50}

\frac{x ^{2} - 49}{x ^{2} + 4 x - 21}

(2 x^{2} + x)^{12}

81 - 9 x^{2}

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