What is (3x^2-12x^3)/(3x^4) ?

The solution to (3x^2-12x^3)/(3x^4) is (1-4x)/(x^2)

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simplify (3x^2-12x^3)/(3x^4)

simplify

\frac{3 x ^{2} - 12 x ^{3}}{3 x ^{4}}

\frac{1 - 4 x}{x ^{2}}

Solution steps

\frac{3 x ^{2} - 12 x ^{3}}{3 x ^{4}}

Factor

3 x^{2} - 12 x^{3} : 3 x^{2} (1 - 4 x)

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

Cancel the common factor:

3

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

Apply exponent rule:

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

x^{4} = x^{2} x^{2}

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

Cancel the common factor:

x^{2}

= \frac{1 - 4 x}{x ^{2}}

[(3 x)^{2}]^{- 2}

(x - 5)^{2} - 2 (x - 5)

\frac{4}{3 - 1}

\frac{1}{x ^{\frac{- 3}{6}}}

\frac{a}{b} + \frac{a}{c}

What is (3x^2-12x^3)/(3x^4) ?
The solution to (3x^2-12x^3)/(3x^4) is (1-4x)/(x^2)