What is simplify+(8a^3-27)/(9-12a+4a^2) ?

The solution to simplify+(8a^3-27)/(9-12a+4a^2) is (4a^2+6a+9)/(2a-3)

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simplify+(8a^3-27)/(9-12a+4a^2)

simplify

+ \frac{8 a ^{3} - 27}{9 - 12 a + 4 a ^{2}}

\frac{4 a ^{2} + 6 a + 9}{2 a - 3}

Solution steps

\frac{8 a ^{3} - 27}{9 - 12 a + 4 a ^{2}}

Factor

8 a^{3} - 27 : (2 a - 3) (4 a^{2} + 6 a + 9)

= \frac{( 2 a - 3 ) ( 4 a ^{2} + 6 a + 9 )}{9 - 12 a + 4 a ^{2}}

Factor

9 - 12 a + 4 a^{2} : (2 a - 3)^{2}

= \frac{( 2 a - 3 ) ( 4 a ^{2} + 6 a + 9 )}{( 2 a - 3 ) ^{2}}

Apply exponent rule:

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

(2 a - 3)^{2} = (2 a - 3) (2 a - 3)

= \frac{( 2 a - 3 ) ( 4 a ^{2} + 6 a + 9 )}{( 2 a - 3 ) ( 2 a - 3 )}

Cancel the common factor:

2 a - 3

= \frac{4 a ^{2} + 6 a + 9}{2 a - 3}

0.00 9^{2}

18 \times \frac{1}{2}

- 2 \times - 2

\frac{6}{9} - \frac{1}{3}

x^{4} + 4 x^{3} - x^{2} - 16 x - 12

What is simplify+(8a^3-27)/(9-12a+4a^2) ?
The solution to simplify+(8a^3-27)/(9-12a+4a^2) is (4a^2+6a+9)/(2a-3)