What is (5x^2)/(20x^4-120x^3) ?

The solution to (5x^2)/(20x^4-120x^3) is 1/(4x(x-6))

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simplify (5x^2)/(20x^4-120x^3)

simplify

\frac{5 x ^{2}}{20 x ^{4} - 120 x ^{3}}

\frac{1}{4 x ( x - 6 )}

Solution steps

\frac{5 x ^{2}}{20 x ^{4} - 120 x ^{3}}

Factor

20 x^{4} - 120 x^{3} : 20 x^{3} (x - 6)

= \frac{5 x ^{2}}{20 x ^{3} ( x - 6 )}

Factor the number:

20 = 5 \cdot 4

= \frac{5 x ^{2}}{5 \cdot 4 x ^{3} ( x - 6 )}

Cancel the common factor:

5

= \frac{x ^{2}}{4 x ^{3} ( x - 6 )}

Apply exponent rule:

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

x^{3} = x^{2} x

= \frac{x ^{2}}{4 x ^{2} x ( x - 6 )}

Cancel the common factor:

x^{2}

= \frac{1}{4 x ( x - 6 )}

(x - 8) (3 x^{2} + 3 x - 1)

\frac{3}{2} \times 5

3 \times (- \frac{1}{3})

52 \times 52

- 6 \times - 3

What is (5x^2)/(20x^4-120x^3) ?
The solution to (5x^2)/(20x^4-120x^3) is 1/(4x(x-6))