What is (x^2-8x+12)/(x^2-16)*(4x+16)/(x^2-4x+4) ?

The solution to (x^2-8x+12)/(x^2-16)*(4x+16)/(x^2-4x+4) is (4(x-6))/((x-4)(x-2))

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simplify (x^2-8x+12)/(x^2-16)*(4x+16)/(x^2-4x+4)

simplify

\frac{x ^{2} - 8 x + 12}{x ^{2} - 16} \cdot \frac{4 x + 16}{x ^{2} - 4 x + 4}

\frac{4 ( x - 6 )}{( x - 4 ) ( x - 2 )}

Solution steps

\frac{x ^{2} - 8 x + 12}{x ^{2} - 16} \cdot \frac{4 x + 16}{x ^{2} - 4 x + 4}

Apply the fraction rule:

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

= \frac{( x ^{2} - 8 x + 12 ) ( 4 x + 16 )}{( x ^{2} - 16 ) ( x ^{2} - 4 x + 4 )}

Factor

x^{2} - 8 x + 12 : (x - 2) (x - 6)

= \frac{( x - 2 ) ( x - 6 ) ( 4 x + 16 )}{( x ^{2} - 16 ) ( x ^{2} - 4 x + 4 )}

Factor

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

= \frac{( x - 2 ) ( x - 6 ) ( 4 x + 16 )}{( x ^{2} - 16 ) ( 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 - 6 ) ( 4 x + 16 )}{( x ^{2} - 16 ) ( x - 2 ) ( x - 2 )}

Cancel the common factor:

x - 2

= \frac{( x - 6 ) ( 4 x + 16 )}{( x ^{2} - 16 ) ( x - 2 )}

Factor

4 x + 16 : 4 (x + 4)

= \frac{( x - 6 ) \cdot 4 ( x + 4 )}{( x ^{2} - 16 ) ( x - 2 )}

Factor

x^{2} - 16 : (x + 4) (x - 4)

= \frac{( x - 6 ) \cdot 4 ( x + 4 )}{( x + 4 ) ( x - 4 ) ( x - 2 )}

Cancel the common factor:

x + 4

= \frac{( x - 6 ) \cdot 4}{( x - 4 ) ( x - 2 )}

= \frac{4 ( x - 6 )}{( x - 4 ) ( x - 2 )}

144 - - 1 - 25 + - 4

(x + 1) \cdot (x + 1)

\frac{x ^{2} + 2 x - 1}{x + 4} - (- x + 3)

ln (128) lo g_{2} (e)

- \frac{7}{2}

What is (x^2-8x+12)/(x^2-16)*(4x+16)/(x^2-4x+4) ?
The solution to (x^2-8x+12)/(x^2-16)*(4x+16)/(x^2-4x+4) is (4(x-6))/((x-4)(x-2))