What is (3x+12)/(x^2+8x+16) ?

The solution to (3x+12)/(x^2+8x+16) is 3/(x+4)

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simplify (3x+12)/(x^2+8x+16)

simplify

\frac{3 x + 12}{x ^{2} + 8 x + 16}

\frac{3}{x + 4}

Solution steps

\frac{3 x + 12}{x ^{2} + 8 x + 16}

Factor

3 x + 12 : 3 (x + 4)

= \frac{3 ( x + 4 )}{x ^{2} + 8 x + 16}

Factor

x^{2} + 8 x + 16 : (x + 4)^{2}

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

Apply exponent rule:

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

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

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

Cancel the common factor:

x + 4

= \frac{3}{x + 4}

4 a^{2} + 7 a - 15

\frac{2 + 7}{2}

32 + 72

2 + 5 x + 6