What is (2a^3-32a)/(2a^3+16a^2+32a) ?

The solution to (2a^3-32a)/(2a^3+16a^2+32a) is (a-4)/(a+4)

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simplify (2a^3-32a)/(2a^3+16a^2+32a)

simplify

\frac{2 a ^{3} - 32 a}{2 a ^{3} + 16 a ^{2} + 32 a}

\frac{a - 4}{a + 4}

Solution steps

\frac{2 a ^{3} - 32 a}{2 a ^{3} + 16 a ^{2} + 32 a}

Factor

2 a^{3} - 32 a : 2 a (a + 4) (a - 4)

= \frac{2 a ( a + 4 ) ( a - 4 )}{2 a ^{3} + 16 a ^{2} + 32 a}

Factor

2 a^{3} + 16 a^{2} + 32 a : 2 a (a + 4)^{2}

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

Cancel the common factor:

2

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

Cancel the common factor:

a

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

Apply exponent rule:

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

(a + 4)^{2} = (a + 4) (a + 4)

= \frac{( a + 4 ) ( a - 4 )}{( a + 4 ) ( a + 4 )}

Cancel the common factor:

a + 4

= \frac{a - 4}{a + 4}

- 8 a b^{2} + a^{2} b + 15 b^{3}

3 x^{3} - 9 x^{2} + 6 x

\frac{1 - i}{- i}

\frac{5 - 4 i}{- 4 + 3 i}

2 (10 b - 3) + 9 = 22 b + 7

What is (2a^3-32a)/(2a^3+16a^2+32a) ?
The solution to (2a^3-32a)/(2a^3+16a^2+32a) is (a-4)/(a+4)