What is (12a^3b^3c^4+18abc^3-24a^2b^2c^8)/(6ab^2c^2) ?

The solution to (12a^3b^3c^4+18abc^3-24a^2b^2c^8)/(6ab^2c^2) is (c(2a^2b^2c+3-4abc^5))/b

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simplify (12a^3b^3c^4+18abc^3-24a^2b^2c^8)/(6ab^2c^2)

simplify

\frac{12 a ^{3} b ^{3} c ^{4} + 18 ab c ^{3} - 24 a ^{2} b ^{2} c ^{8}}{6 a b ^{2} c ^{2}}

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

Solution steps

\frac{12 a ^{3} b ^{3} c ^{4} + 18 ab c ^{3} - 24 a ^{2} b ^{2} c ^{8}}{6 a b ^{2} c ^{2}}

Factor out common term

6 ab c^{3} : 6 ab c^{3} (2 a^{2} b^{2} c + 3 - 4 ab c^{5})

= \frac{6 ab c ^{3} ( 2 a ^{2} b ^{2} c + 3 - 4 ab c ^{5} )}{6 a b ^{2} c ^{2}}

Cancel the common factor:

6

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

Cancel the common factor:

a

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

Apply exponent rule:

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

c^{3} = c^{2} c

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

Cancel the common factor:

c^{2}

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

Apply exponent rule:

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

b^{2} = bb

= \frac{b c ( 2 a ^{2} b ^{2} c + 3 - 4 ab c ^{5} )}{bb}

Cancel the common factor:

b

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

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What is (12a^3b^3c^4+18abc^3-24a^2b^2c^8)/(6ab^2c^2) ?
The solution to (12a^3b^3c^4+18abc^3-24a^2b^2c^8)/(6ab^2c^2) is (c(2a^2b^2c+3-4abc^5))/b