What is (2x+6)/(5x+10)*(x+2)/(x^2+4x+3) ?

The solution to (2x+6)/(5x+10)*(x+2)/(x^2+4x+3) is 2/(5(x+1))

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simplify (2x+6)/(5x+10)*(x+2)/(x^2+4x+3)

simplify

\frac{2 x + 6}{5 x + 10} \cdot \frac{x + 2}{x ^{2} + 4 x + 3}

\frac{2}{5 ( x + 1 )}

Solution steps

\frac{2 x + 6}{5 x + 10} \cdot \frac{x + 2}{x ^{2} + 4 x + 3}

Apply the fraction rule:

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

= \frac{( 2 x + 6 ) ( x + 2 )}{( 5 x + 10 ) ( x ^{2} + 4 x + 3 )}

Factor

5 x + 10 : 5 (x + 2)

= \frac{( 2 x + 6 ) ( x + 2 )}{5 ( x + 2 ) ( x ^{2} + 4 x + 3 )}

Cancel the common factor:

x + 2

= \frac{2 x + 6}{5 ( x ^{2} + 4 x + 3 )}

Factor

2 x + 6 : 2 (x + 3)

= \frac{2 ( x + 3 )}{5 ( x ^{2} + 4 x + 3 )}

Factor

x^{2} + 4 x + 3 : (x + 1) (x + 3)

= \frac{2 ( x + 3 )}{5 ( x + 1 ) ( x + 3 )}

Cancel the common factor:

x + 3

= \frac{2}{5 ( x + 1 )}

9 x^{5}

(x^{2} - 16)^{2}

\frac{x + h + x}{h x - 2 h}

\frac{2 x ^{2} - x y - 6 y ^{2}}{3 x ^{2} - 5 x y - 2 y ^{2}}

8 \times (- 2)

What is (2x+6)/(5x+10)*(x+2)/(x^2+4x+3) ?
The solution to (2x+6)/(5x+10)*(x+2)/(x^2+4x+3) is 2/(5(x+1))