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

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

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simplify (x^2+5x+6)/(x^2+4x+4)

simplify

\frac{x ^{2} + 5 x + 6}{x ^{2} + 4 x + 4}

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

Solution steps

\frac{x ^{2} + 5 x + 6}{x ^{2} + 4 x + 4}

Factor

x^{2} + 5 x + 6 : (x + 2) (x + 3)

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

Factor

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

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

Apply exponent rule:

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

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

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

Cancel the common factor:

x + 2

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

- 24 a^{2} b^{2} + 36 ab - 60 a

6 c b + 4 b c + 13 c + 9 + 9 c

\frac{1}{( - 4.999 ) ^{2} - 25}

(x - 1)^{3} - 1

- r + 6 + 8 r - 14

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