What is ((x^2+4x)/(2x+6))((2x+4)/(x+4)) ?

The solution to ((x^2+4x)/(2x+6))((2x+4)/(x+4)) is (x(x+2))/(x+3)

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simplify ((x^2+4x)/(2x+6))((2x+4)/(x+4))

simplify

(\frac{x ^{2} + 4 x}{2 x + 6}) (\frac{2 x + 4}{x + 4})

\frac{x ( x + 2 )}{x + 3}

Solution steps

(\frac{x ^{2} + 4 x}{2 x + 6}) (\frac{2 x + 4}{x + 4})

Simplify

(\frac{x ^{2} + 4 x}{2 x + 6}) (\frac{2 x + 4}{x + 4}) : \frac{x ^{2} + 4 x}{2 x + 6} \cdot \frac{2 x + 4}{x + 4}

= \frac{x ^{2} + 4 x}{2 x + 6} \cdot \frac{2 x + 4}{x + 4}

Apply the fraction rule:

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

= \frac{( x ^{2} + 4 x ) ( 2 x + 4 )}{( 2 x + 6 ) ( x + 4 )}

Factor

x^{2} + 4 x : x (x + 4)

= \frac{x ( x + 4 ) ( 2 x + 4 )}{( 2 x + 6 ) ( x + 4 )}

Cancel the common factor:

x + 4

= \frac{x ( 2 x + 4 )}{2 x + 6}

Factor

2 x + 4 : 2 (x + 2)

= \frac{x \cdot 2 ( x + 2 )}{2 x + 6}

Factor

2 x + 6 : 2 (x + 3)

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

Cancel the common factor:

2

= \frac{x ( x + 2 )}{x + 3}

- \frac{1}{x} - 1

\frac{a ^{3} b ^{- 5} c ^{- 1}}{c ^{- 4} b a ^{- 4}}

\frac{2}{6} + \frac{1}{7}

x^{3} + 4 x^{2} + 6 x + 4

(5 x + 8) (5 x - 8)

What is ((x^2+4x)/(2x+6))((2x+4)/(x+4)) ?
The solution to ((x^2+4x)/(2x+6))((2x+4)/(x+4)) is (x(x+2))/(x+3)