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

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

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

simplify

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

\frac{x + 1}{x}

Solution steps

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

Apply cube of sum rule:

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

x^{3} + 3 x^{2} + 3 x + 1 = (x + 1)^{3}

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

Factor

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

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

Apply exponent rule:

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

(x + 1)^{3} = (x + 1)^{2} (x + 1)

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

Cancel the common factor:

(x + 1)^{2}

= \frac{x + 1}{x}

(x^{2} - \frac{3}{2})^{2}

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

(2 x y)^{4}

- 3 \frac{1}{2} \div \frac{4}{9}

(x^{2} + 6 x - 15) - (4 x^{2} - 3 x - 5)

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