What is (x^3-1)/(x^2-2x+1) ?

The solution to (x^3-1)/(x^2-2x+1) is (x^2+x+1)/(x-1)

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simplify (x^3-1)/(x^2-2x+1)

simplify

\frac{x ^{3} - 1}{x ^{2} - 2 x + 1}

\frac{x ^{2} + x + 1}{x - 1}

Solution steps

\frac{x ^{3} - 1}{x ^{2} - 2 x + 1}

Factor

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

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

Factor

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

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

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

(x - 1)^{2} = (x - 1) (x - 1)

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

Cancel the common factor:

x - 1

= \frac{x ^{2} + x + 1}{x - 1}

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

lo g_{6} (\frac{1}{1296})

f (a)

(1 + t^{2})^{2}

1 7^{l o g_{17} (2)}

What is (x^3-1)/(x^2-2x+1) ?
The solution to (x^3-1)/(x^2-2x+1) is (x^2+x+1)/(x-1)