What is ((3x+9))/((5x^2y))*((x^3y^2))/((2x+6)) ?

The solution to ((3x+9))/((5x^2y))*((x^3y^2))/((2x+6)) is (3xy)/(10)

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simplify ((3x+9))/((5x^2y))*((x^3y^2))/((2x+6))

simplify

\frac{( 3 x + 9 )}{( 5 x ^{2} y )} \cdot \frac{( x ^{3} y ^{2} )}{( 2 x + 6 )}

\frac{3 x y}{10}

Solution steps

\frac{3 x + 9}{5 x ^{2} y} \cdot \frac{x ^{3} y ^{2}}{2 x + 6}

Apply the fraction rule:

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

= \frac{( 3 x + 9 ) x ^{3} y ^{2}}{5 x ^{2} y ( 2 x + 6 )}

Apply exponent rule:

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

x^{3} = x^{2} x

= \frac{( 3 x + 9 ) x ^{2} x y ^{2}}{5 x ^{2} y ( 2 x + 6 )}

Cancel the common factor:

x^{2}

= \frac{( 3 x + 9 ) x y ^{2}}{5 y ( 2 x + 6 )}

Apply exponent rule:

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

y^{2} = yy

= \frac{( 3 x + 9 ) x yy}{5 y ( 2 x + 6 )}

Cancel the common factor:

y

= \frac{( 3 x + 9 ) x y}{5 ( 2 x + 6 )}

Factor

3 x + 9 : 3 (x + 3)

= \frac{3 ( x + 3 ) x y}{5 ( 2 x + 6 )}

Factor

2 x + 6 : 2 (x + 3)

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

Cancel the common factor:

x + 3

= \frac{3 x y}{5 \cdot 2}

Multiply the numbers:

5 \cdot 2 = 10

= \frac{3 x y}{10}

\frac{5 ! + 6 ! + 7 !}{5 ! + 6 !}

3 - 0.01 (200) + 0.00006 (200)^{2}

- \frac{6}{4} - \frac{2}{4}

(4 x - 2) (4 x + 6)

7 \frac{2}{5} - 5 \frac{2}{3}

What is ((3x+9))/((5x^2y))*((x^3y^2))/((2x+6)) ?
The solution to ((3x+9))/((5x^2y))*((x^3y^2))/((2x+6)) is (3xy)/(10)