What is ((a^3-2a^2*b))/((2a^3*b^2-a^4*b)) ?

The solution to ((a^3-2a^2*b))/((2a^3*b^2-a^4*b)) is -1/(ab)

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simplify ((a^3-2a^2b))/((2a^3b^2-a^4*b))

simplify

\frac{( a ^{3} - 2 a ^{2} \cdot b )}{( 2 a ^{3} \cdot b ^{2} - a ^{4} \cdot b )}

- \frac{1}{ab}

Solution steps

\frac{a ^{3} - 2 a ^{2} b}{2 a ^{3} b ^{2} - a ^{4} b}

Factor

a^{3} - 2 a^{2} b : a^{2} (a - 2 b)

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

Factor

2 a^{3} b^{2} - a^{4} b : a^{3} b (2 b - a)

= \frac{a ^{2} ( a - 2 b )}{a ^{3} b ( 2 b - a )}

Apply exponent rule:

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

a^{3} = a^{2} a

= \frac{a ^{2} ( a - 2 b )}{a ^{2} ab ( 2 b - a )}

Cancel the common factor:

a^{2}

= \frac{a - 2 b}{ab ( 2 b - a )}

ab (2 b - a) = - ab (a - 2 b)

= \frac{a - 2 b}{- ab ( a - 2 b )}

Cancel the common factor:

a - 2 b

= \frac{1}{- ab}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{1}{ab}

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x \cdot 10 x

(57.8)^{\frac{1}{2}} x (0.0027)^{\frac{1}{3}}

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What is ((a^3-2a^2*b))/((2a^3*b^2-a^4*b)) ?
The solution to ((a^3-2a^2*b))/((2a^3*b^2-a^4*b)) is -1/(ab)