What is (x^2y)/(x-9)*(x^2-81)/(xy^2) ?

The solution to (x^2y)/(x-9)*(x^2-81)/(xy^2) is (x(x+9))/y

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simplify (x^2y)/(x-9)*(x^2-81)/(xy^2)

simplify

\frac{x ^{2} y}{x - 9} \cdot \frac{x ^{2} - 81}{x y ^{2}}

\frac{x ( x + 9 )}{y}

Solution steps

\frac{x ^{2} y}{x - 9} \cdot \frac{x ^{2} - 81}{x y ^{2}}

Apply the fraction rule:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

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

Apply exponent rule:

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

x^{2} = xx

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

Cancel the common factor:

x

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

Apply exponent rule:

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

y^{2} = yy

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

Cancel the common factor:

y

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

Factor

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

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

Cancel the common factor:

x - 9

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

3 < - 5 x + 8 < 10

y^{\frac{3}{4}} \cdot y^{\frac{1}{3}}

3 t^{2} - 24 t + 36 = 0

x^{4} - 3 x^{2} - 28

- 3 b - 4 \leq 3 b + 3

What is (x^2y)/(x-9)*(x^2-81)/(xy^2) ?
The solution to (x^2y)/(x-9)*(x^2-81)/(xy^2) is (x(x+9))/y