What is (x^2-3x}{x-2}*\frac{x^2+x-6)/x ?

The solution to (x^2-3x}{x-2}*\frac{x^2+x-6)/x is (x-3)(x+3)

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simplify (x^2-3x}{x-2}*\frac{x^2+x-6)/x

simplify

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

(x - 3) (x + 3)

Solution steps

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

Apply the fraction rule:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

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

Factor

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

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

Cancel the common factor:

x

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

Factor

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

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

Cancel the common factor:

x - 2

= (x - 3) (x + 3)

(a^{- 2} - b^{- 2})^{- 1}

(1 6^{3}) \frac{1}{4}

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

\frac{x ^{12}}{x ^{3}}

\frac{- a ^{2} b}{- ab}

What is (x^2-3x}{x-2}*\frac{x^2+x-6)/x ?
The solution to (x^2-3x}{x-2}*\frac{x^2+x-6)/x is (x-3)(x+3)