What is (x^2+6x+9)/(2x^2+8x+6) ?

The solution to (x^2+6x+9)/(2x^2+8x+6) is (x+3)/(2(x+1))

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simplify (x^2+6x+9)/(2x^2+8x+6)

simplify

\frac{x ^{2} + 6 x + 9}{2 x ^{2} + 8 x + 6}

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

Solution steps

\frac{x ^{2} + 6 x + 9}{2 x ^{2} + 8 x + 6}

Factor

x^{2} + 6 x + 9 : (x + 3)^{2}

= \frac{( x + 3 ) ^{2}}{2 x ^{2} + 8 x + 6}

Factor

2 x^{2} + 8 x + 6 : 2 (x + 1) (x + 3)

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

Apply exponent rule:

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

(x + 3)^{2} = (x + 3) (x + 3)

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

Cancel the common factor:

x + 3

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

f (x + 1)

\frac{1}{16}

(x - 1) (3 x^{2} + 7 x + 5)

(x^{2} + y^{2}) (x^{2} - y^{2})

\frac{56}{8}

What is (x^2+6x+9)/(2x^2+8x+6) ?
The solution to (x^2+6x+9)/(2x^2+8x+6) is (x+3)/(2(x+1))