What is (5x^2+20xy+20y^2)/(x^2-xy-6y^2) ?

The solution to (5x^2+20xy+20y^2)/(x^2-xy-6y^2) is (5(x+2y))/(x-3y)

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simplify (5x^2+20xy+20y^2)/(x^2-xy-6y^2)

simplify

\frac{5 x ^{2} + 20 x y + 20 y ^{2}}{x ^{2} - x y - 6 y ^{2}}

\frac{5 ( x + 2 y )}{x - 3 y}

Solution steps

\frac{5 x ^{2} + 20 x y + 20 y ^{2}}{x ^{2} - x y - 6 y ^{2}}

Factor

5 x^{2} + 20 x y + 20 y^{2} : 5 (x + 2 y)^{2}

= \frac{5 ( x + 2 y ) ^{2}}{x ^{2} - x y - 6 y ^{2}}

Factor

x^{2} - x y - 6 y^{2} : (x + 2 y) (x - 3 y)

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

Apply exponent rule:

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

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

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

Cancel the common factor:

x + 2 y

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

- x^{2} + 2 x

\frac{5}{9} (68 - 32)

0 = \frac{x}{10} - \frac{x ^{2}}{1800000}

8 x^{5} + 4 x^{3}

- 4 \geq \frac{2 - 5 x}{4}

What is (5x^2+20xy+20y^2)/(x^2-xy-6y^2) ?
The solution to (5x^2+20xy+20y^2)/(x^2-xy-6y^2) is (5(x+2y))/(x-3y)