What is (1-6/y+9/(y^2))(2-6/(y+3))y ?

The solution to (1-6/y+9/(y^2))(2-6/(y+3))y is (2(y^2-6y+9))/(y+3)

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simplify (1-6/y+9/(y^2))(2-6/(y+3))y

simplify

(1 - \frac{6}{y} + \frac{9}{y ^{2}}) (2 - \frac{6}{y + 3}) y

\frac{2 ( y ^{2} - 6 y + 9 )}{y + 3}

Solution steps

(1 - \frac{6}{y} + \frac{9}{y ^{2}}) (2 - \frac{6}{y + 3}) y

Join

1 - \frac{6}{y} + \frac{9}{y ^{2}} : \frac{y ^{2} - 6 y + 9}{y ^{2}}

= \frac{y ^{2} - 6 y + 9}{y ^{2}} (2 - \frac{6}{y + 3}) y

Apply the fraction rule:

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

= \frac{( y ^{2} - 6 y + 9 ) ( 2 - \frac{6}{y + 3} ) y}{y ^{2}}

Apply exponent rule:

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

y^{2} = yy

= \frac{( y ^{2} - 6 y + 9 ) ( 2 - \frac{6}{y + 3} ) y}{yy}

Cancel the common factor:

y

= \frac{( y ^{2} - 6 y + 9 ) ( 2 - \frac{6}{y + 3} )}{y}

Simplify

(y^{2} - 6 y + 9) (2 - \frac{6}{y + 3}) : \frac{( y ^{2} - 6 y + 9 ) \cdot 2 y}{y + 3}

= \frac{\frac{( y ^{2} - 6 y + 9 ) \cdot 2 y}{y + 3}}{y}

Apply the fraction rule:

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

= \frac{( y ^{2} - 6 y + 9 ) \cdot 2 y}{( y + 3 ) y}

Cancel the common factor:

y

= \frac{( y ^{2} - 6 y + 9 ) \cdot 2}{y + 3}

= \frac{2 ( y ^{2} - 6 y + 9 )}{y + 3}

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\frac{x + 1}{x ( x - 1 )}

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What is (1-6/y+9/(y^2))(2-6/(y+3))y ?
The solution to (1-6/y+9/(y^2))(2-6/(y+3))y is (2(y^2-6y+9))/(y+3)