What is (x^2-9)/(x^2+x-20)*(x^2-8x+16)/(3x-9) ?

The solution to (x^2-9)/(x^2+x-20)*(x^2-8x+16)/(3x-9) is ((x+3)(x-4))/(3(x+5))

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simplify (x^2-9)/(x^2+x-20)*(x^2-8x+16)/(3x-9)

simplify

\frac{x ^{2} - 9}{x ^{2} + x - 20} \cdot \frac{x ^{2} - 8 x + 16}{3 x - 9}

\frac{( x + 3 ) ( x - 4 )}{3 ( x + 5 )}

Solution steps

\frac{x ^{2} - 9}{x ^{2} + x - 20} \cdot \frac{x ^{2} - 8 x + 16}{3 x - 9}

Apply the fraction rule:

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

= \frac{( x ^{2} - 9 ) ( x ^{2} - 8 x + 16 )}{( x ^{2} + x - 20 ) ( 3 x - 9 )}

Factor

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

= \frac{( x + 3 ) ( x - 3 ) ( x ^{2} - 8 x + 16 )}{( x ^{2} + x - 20 ) ( 3 x - 9 )}

Factor

3 x - 9 : 3 (x - 3)

= \frac{( x + 3 ) ( x - 3 ) ( x ^{2} - 8 x + 16 )}{( x ^{2} + x - 20 ) \cdot 3 ( x - 3 )}

Cancel the common factor:

x - 3

= \frac{( x + 3 ) ( x ^{2} - 8 x + 16 )}{( x ^{2} + x - 20 ) \cdot 3}

Factor

x^{2} - 8 x + 16 : (x - 4)^{2}

= \frac{( x + 3 ) ( x - 4 ) ^{2}}{( x ^{2} + x - 20 ) \cdot 3}

Factor

x^{2} + x - 20 : (x - 4) (x + 5)

= \frac{( x + 3 ) ( x - 4 ) ^{2}}{( x - 4 ) ( x + 5 ) \cdot 3}

Apply exponent rule:

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

(x - 4)^{2} = (x - 4) (x - 4)

= \frac{( x + 3 ) ( x - 4 ) ( x - 4 )}{( x - 4 ) ( x + 5 ) \cdot 3}

Cancel the common factor:

x - 4

= \frac{( x + 3 ) ( x - 4 )}{( x + 5 ) \cdot 3}

= \frac{( x + 3 ) ( x - 4 )}{3 ( x + 5 )}

(x) (x + 2)

\frac{1}{2} + \frac{1}{3} + \frac{5}{6}

7 \times (- 3)

28 - 21 x

2 x - 2 x^{2}

What is (x^2-9)/(x^2+x-20)*(x^2-8x+16)/(3x-9) ?
The solution to (x^2-9)/(x^2+x-20)*(x^2-8x+16)/(3x-9) is ((x+3)(x-4))/(3(x+5))