What is (81x^2-y^2)/(3sqrt(x)+\sqrt{y)} ?

The solution to (81x^2-y^2)/(3sqrt(x)+\sqrt{y)} is (9x+y)(3sqrt(x)-sqrt(y))

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simplify (81x^2-y^2)/(3sqrt(x)+\sqrt{y)}

simplify

\frac{81 x ^{2} - y ^{2}}{3 x + y}

(9 x + y) (3 x - y)

Solution steps

\frac{81 x ^{2} - y ^{2}}{3 x + y}

Multiply by the conjugate

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

= \frac{( 81 x ^{2} - y ^{2} ) ( 3 x - y )}{( 3 x + y ) ( 3 x - y )}

(3 x + y) (3 x - y) = 9 x - y

= \frac{( 81 x ^{2} - y ^{2} ) ( 3 x - y )}{9 x - y}

Factor

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

= \frac{( 9 x + y ) ( 9 x - y ) ( 3 x - y )}{9 x - y}

Cancel the common factor:

9 x - y

= (9 x + y) (3 x - y)

x^{2} - 6 x + 7 = - 2

- 3 (y + 4) + 6 y = 24

\frac{x}{2} - \frac{1}{3} = \frac{x}{3} + \frac{5}{6}

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

a^{2} + 9^{2} = 1 0^{2}

What is (81x^2-y^2)/(3sqrt(x)+\sqrt{y)} ?
The solution to (81x^2-y^2)/(3sqrt(x)+\sqrt{y)} is (9x+y)(3sqrt(x)-sqrt(y))