What is (3sqrt(11x^3y))/(-2sqrt(12x^4y)) ?

The solution to (3sqrt(11x^3y))/(-2sqrt(12x^4y)) is -(sqrt(33))/(4sqrt(x))

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simplify (3sqrt(11x^3y))/(-2sqrt(12x^4y))

simplify

\frac{3 11 x ^{3} y}{- 2 12 x ^{4} y}

- \frac{33}{4 x}

Solution steps

\frac{3 11 x ^{3} y}{- 2 12 x ^{4} y}

Apply radical rule:

ab = a b,

assuming

a \geq 0, b \geq 0

11 x^{3} y = y 11 x^{3}

= \frac{3 y 11 x ^{3}}{- 2 12 x ^{4} y}

Apply radical rule:

ab = a b,

assuming

a \geq 0, b \geq 0

12 x^{4} y = y 12 x^{4}

= \frac{3 y 11 x ^{3}}{- 2 y 12 x ^{4}}

Cancel the common factor:

y

= \frac{3 11 x ^{3}}{- 2 12 x ^{4}}

Apply radical rule:

ab = a b,

assuming

a \geq 0, b \geq 0

12 x^{4} = 12 x^{4}

= \frac{3 11 x ^{3}}{- 2 12 x ^{4}}

Factor

12 : 3 \cdot 2

= \frac{3 11 x ^{3}}{- 2 3 \cdot 2 x ^{4}}

Apply radical rule:

a = a a

3 = 33

= \frac{3 3 11 x ^{3}}{- 2 3 \cdot 2 x ^{4}}

Cancel the common factor:

3

= \frac{3 11 x ^{3}}{- 2 \cdot 2 x ^{4}}

Apply radical rule:

ab = a b,

assuming

a \geq 0, b \geq 0

11 x^{3} = x^{3} 11

= \frac{3 x ^{3} 11}{- 2 \cdot 2 x ^{4}}

Apply exponent rule:

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

x^{4} = x^{3} x

= \frac{3 x ^{3} 11}{- 2 \cdot 2 x ^{3} x}

Apply radical rule:

ab = a b,

assuming

a \geq 0, b \geq 0

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

= \frac{3 x ^{3} 11}{- 2 \cdot 2 x ^{3} x}

Cancel the common factor:

x^{3}

= \frac{3 11}{- 2 \cdot 2 x}

Simplify

\frac{3 11}{- 2 \cdot 2 x} : - \frac{33}{4 x}

= - \frac{33}{4 x}

- 5 x + 17 = 27

0.5 y = 19.5

(x - 1)^{2} + 11 x + 199 = 3 x^{2} - (x - 2)^{2}

\frac{72}{8}

2 x^{- 1}

What is (3sqrt(11x^3y))/(-2sqrt(12x^4y)) ?
The solution to (3sqrt(11x^3y))/(-2sqrt(12x^4y)) is -(sqrt(33))/(4sqrt(x))