What is (3x^2-12xy+12y^2)/(30y^2-15xy) ?

The solution to (3x^2-12xy+12y^2)/(30y^2-15xy) is -(x-2y)/(5y)

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simplify (3x^2-12xy+12y^2)/(30y^2-15xy)

simplify

\frac{3 x ^{2} - 12 x y + 12 y ^{2}}{30 y ^{2} - 15 x y}

- \frac{x - 2 y}{5 y}

Solution steps

\frac{3 x ^{2} - 12 x y + 12 y ^{2}}{30 y ^{2} - 15 x y}

Factor

3 x^{2} - 12 x y + 12 y^{2} : 3 (x - 2 y)^{2}

= \frac{3 ( x - 2 y ) ^{2}}{30 y ^{2} - 15 x y}

Factor

30 y^{2} - 15 x y : 15 y (2 y - x)

= \frac{3 ( x - 2 y ) ^{2}}{15 y ( 2 y - x )}

Factor the number:

15 = 3 \cdot 5

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

Cancel the common factor:

3

= \frac{( x - 2 y ) ^{2}}{5 y ( 2 y - x )}

5 y (2 y - x) = - 5 y (x - 2 y)

= \frac{( x - 2 y ) ^{2}}{- 5 y ( x - 2 y )}

Apply exponent rule:

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

(x - 2 y)^{2} = (x - 2 y) (x - 2 y)

= \frac{( x - 2 y ) ( x - 2 y )}{- 5 y ( x - 2 y )}

Cancel the common factor:

x - 2 y

= \frac{x - 2 y}{- 5 y}

Apply the fraction rule:

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

= - \frac{x - 2 y}{5 y}

3 x^{2} + 27 x - 30

\frac{1}{1 + \frac{1}{1 + \frac{1}{2}}}

2 x^{2} y - 2 x y^{2} + 4 x y

2 x^{2} + 10 x + 1 = 0

3 x - 91 > - 87 and 17 x - 16 > 18

What is (3x^2-12xy+12y^2)/(30y^2-15xy) ?
The solution to (3x^2-12xy+12y^2)/(30y^2-15xy) is -(x-2y)/(5y)