What is (x^3-9x)/(x^3-6x^2+9x) ?

The solution to (x^3-9x)/(x^3-6x^2+9x) is (x+3)/(x-3)

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simplify (x^3-9x)/(x^3-6x^2+9x)

simplify

\frac{x ^{3} - 9 x}{x ^{3} - 6 x ^{2} + 9 x}

\frac{x + 3}{x - 3}

Solution steps

\frac{x ^{3} - 9 x}{x ^{3} - 6 x ^{2} + 9 x}

Factor

x^{3} - 9 x : x (x + 3) (x - 3)

= \frac{x ( x + 3 ) ( x - 3 )}{x ^{3} - 6 x ^{2} + 9 x}

Factor

x^{3} - 6 x^{2} + 9 x : x (x - 3)^{2}

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

Cancel the common factor:

x

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

Apply exponent rule:

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

(x - 3)^{2} = (x - 3) (x - 3)

= \frac{( x + 3 ) ( x - 3 )}{( x - 3 ) ( x - 3 )}

Cancel the common factor:

x - 3

= \frac{x + 3}{x - 3}

\frac{\frac{x ^{3} - 121 x}{x ^{2} - 49}}{\frac{x ^{2} - 11 x}{x + 7}}

- 6 \cdot 4

63 x^{3} y^{4}

2 x \times 3 x

(x - 3)^{2} + (y - 4)^{2}

What is (x^3-9x)/(x^3-6x^2+9x) ?
The solution to (x^3-9x)/(x^3-6x^2+9x) is (x+3)/(x-3)