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

The solution to (x+3)/(x^2-4x+4)*(x^2-x-2)/(x^2+4x+3) is 1/(x-2)

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

simplify

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

\frac{1}{x - 2}

Solution steps

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

Cancel

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

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

Cross-cancel common factor:

x + 3

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

Factor

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

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

Apply exponent rule:

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

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

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

Cancel the common factor:

x - 2

= \frac{1}{x - 2}

12 x^{3} - 12 x^{2} - 24 x

r + (- 5 r)

g (4)

g (t)

(x - 2) (x + 5)

What is (x+3)/(x^2-4x+4)*(x^2-x-2)/(x^2+4x+3) ?
The solution to (x+3)/(x^2-4x+4)*(x^2-x-2)/(x^2+4x+3) is 1/(x-2)