What is (-8x^2-48xy-72y^2)/(2x^2-18y^2) ?

The solution to (-8x^2-48xy-72y^2)/(2x^2-18y^2) is -(4(x+3y))/(x-3y)

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simplify (-8x^2-48xy-72y^2)/(2x^2-18y^2)

simplify

\frac{- 8 x ^{2} - 48 x y - 72 y ^{2}}{2 x ^{2} - 18 y ^{2}}

- \frac{4 ( x + 3 y )}{x - 3 y}

Solution steps

\frac{- 8 x ^{2} - 48 x y - 72 y ^{2}}{2 x ^{2} - 18 y ^{2}}

Factor

- 8 x^{2} - 48 x y - 72 y^{2} : - 8 (x + 3 y)^{2}

= \frac{- 8 ( x + 3 y ) ^{2}}{2 x ^{2} - 18 y ^{2}}

Factor

2 x^{2} - 18 y^{2} : 2 (x + 3 y) (x - 3 y)

= \frac{- 8 ( x + 3 y ) ^{2}}{2 ( x + 3 y ) ( x - 3 y )}

Factor the number:

8 = 2 \cdot 4

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

Cancel the common factor:

2

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

Apply exponent rule:

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

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

= \frac{- 4 ( x + 3 y ) ( x + 3 y )}{( x + 3 y ) ( x - 3 y )}

Cancel the common factor:

x + 3 y

= \frac{- 4 ( x + 3 y )}{x - 3 y}

Apply the fraction rule:

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

= - \frac{4 ( x + 3 y )}{x - 3 y}

6 - 2 x = 10

\frac{2 ( 1 )}{1 + 1}

\frac{1}{x} < 1

∣ x + 3 ∣ \geq 3

- 4 = \frac{4}{17} \cdot \frac{1}{2} + b

What is (-8x^2-48xy-72y^2)/(2x^2-18y^2) ?
The solution to (-8x^2-48xy-72y^2)/(2x^2-18y^2) is -(4(x+3y))/(x-3y)