What is (9x^2+4y^2-12xy)/(4y^2-9x^2) ?

The solution to (9x^2+4y^2-12xy)/(4y^2-9x^2) is -(3x-2y)/(2y+3x)

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simplify (9x^2+4y^2-12xy)/(4y^2-9x^2)

simplify

\frac{9 x ^{2} + 4 y ^{2} - 12 x y}{4 y ^{2} - 9 x ^{2}}

- \frac{3 x - 2 y}{2 y + 3 x}

Solution steps

\frac{9 x ^{2} + 4 y ^{2} - 12 x y}{4 y ^{2} - 9 x ^{2}}

Factor

9 x^{2} + 4 y^{2} - 12 x y : (3 x - 2 y)^{2}

= \frac{( 3 x - 2 y ) ^{2}}{4 y ^{2} - 9 x ^{2}}

Factor

4 y^{2} - 9 x^{2} : (2 y + 3 x) (2 y - 3 x)

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

(2 y + 3 x) (2 y - 3 x) = - (2 y + 3 x) (3 x - 2 y)

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

Apply exponent rule:

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

(3 x - 2 y)^{2} = (3 x - 2 y) (3 x - 2 y)

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

Cancel the common factor:

3 x - 2 y

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

Apply the fraction rule:

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

= - \frac{3 x - 2 y}{2 y + 3 x}

2 a + \frac{1}{2} = \frac{1}{4}

7 x^{2} - 5 x - 2

\frac{27}{2} \cdot 78400

3 x - 9 = 12

\frac{x ^{2}}{x + 2} < \frac{12 - x}{x + 2}

What is (9x^2+4y^2-12xy)/(4y^2-9x^2) ?
The solution to (9x^2+4y^2-12xy)/(4y^2-9x^2) is -(3x-2y)/(2y+3x)