What is (3x+9)/2*1/(3x^2-27) ?

The solution to (3x+9)/2*1/(3x^2-27) is 1/(2(x-3))

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simplify (3x+9)/2*1/(3x^2-27)

simplify

\frac{3 x + 9}{2} \cdot \frac{1}{3 x ^{2} - 27}

\frac{1}{2 ( x - 3 )}

Solution steps

\frac{3 x + 9}{2} \cdot \frac{1}{3 x ^{2} - 27}

Apply the fraction rule:

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

= \frac{( 3 x + 9 ) \cdot 1}{2 ( 3 x ^{2} - 27 )}

Apply rule:

a \cdot 1 = a

(3 x + 9) \cdot 1 = (3 x + 9)

= \frac{3 x + 9}{2 ( 3 x ^{2} - 27 )}

Factor

3 x + 9 : 3 (x + 3)

= \frac{3 ( x + 3 )}{2 ( 3 x ^{2} - 27 )}

Factor

3 x^{2} - 27 : 3 (x + 3) (x - 3)

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

Cancel the common factor:

3

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

Cancel the common factor:

x + 3

= \frac{1}{2 ( x - 3 )}

\frac{2 + 3 i}{1 + i}

2 x (x + 3)

(- 7 + i)^{2}

(- x + 3)^{2}

(2 a - 1) (1 + 2 a)

What is (3x+9)/2*1/(3x^2-27) ?
The solution to (3x+9)/2*1/(3x^2-27) is 1/(2(x-3))