What is ((9a^9-9a^7+18a^4))/((15a^8)) ?

The solution to ((9a^9-9a^7+18a^4))/((15a^8)) is (3(a^5-a^3+2))/(5a^4)

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simplify ((9a^9-9a^7+18a^4))/((15a^8))

simplify

\frac{( 9 a ^{9} - 9 a ^{7} + 18 a ^{4} )}{( 15 a ^{8} )}

\frac{3 ( a ^{5} - a ^{3} + 2 )}{5 a ^{4}}

Solution steps

\frac{9 a ^{9} - 9 a ^{7} + 18 a ^{4}}{15 a ^{8}}

Factor

9 a^{9} - 9 a^{7} + 18 a^{4} : 9 a^{4} (a^{5} - a^{3} + 2)

= \frac{9 a ^{4} ( a ^{5} - a ^{3} + 2 )}{15 a ^{8}}

Factor the number:

9 = 3 \cdot 3

= \frac{3 \cdot 3 a ^{4} ( a ^{5} - a ^{3} + 2 )}{15 a ^{8}}

Factor the number:

15 = 3 \cdot 5

= \frac{3 \cdot 3 a ^{4} ( a ^{5} - a ^{3} + 2 )}{3 \cdot 5 a ^{8}}

Cancel the common factor:

3

= \frac{3 a ^{4} ( a ^{5} - a ^{3} + 2 )}{5 a ^{8}}

Apply exponent rule:

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

a^{8} = a^{4} a^{4}

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

Cancel the common factor:

a^{4}

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

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

(- 4 x^{3})^{2} \cdot (8 x^{4})^{- 1}

(p^{- 1} + q^{- 1})^{- 1}

4 x^{3} - 12 x - 4

(1 - 2 x) (4 + 3 x)

What is ((9a^9-9a^7+18a^4))/((15a^8)) ?
The solution to ((9a^9-9a^7+18a^4))/((15a^8)) is (3(a^5-a^3+2))/(5a^4)