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

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

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

simplify

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

\frac{x}{x + 3}

Solution steps

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

Factor

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

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

Factor

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

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

Apply the commutative law:

2 + x = x + 2

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

Cancel the common factor:

x + 2

= \frac{x}{x + 3}

\frac{5 x ^{2} - 15 x}{x ^{2} + 2 x - 15}

(2 x - 3) (3 x + 1)

- 2 x^{2} - 32 x - 30

2 + 4 + 8 + 16 + 32 + 2^{n}