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Ratling [72]
3 years ago
15

Simplify the expression given below. x+2/X^3+2x^2-9x-18 divided by 3x +1/x^2-9

Mathematics
1 answer:
ratelena [41]3 years ago
8 0
Answer:

\frac{1}{3x+1}

Explanation:

1) Expression given:

\frac{ \frac{x+2}{x^3+2x^2-9x-18} }{ \frac{3x+1}{x^2-9} }

2) Factor the denominator of the first fraction:

x^3+2x^2-9x-18=(x^3+2x^2)-(9x+18)=x^2(x+2)-9(x+2)=

(x+2)(x^2-9)

3) Rewrite the expression

\frac{ \frac{x+2}{(x+2)(x^2-9)} }{ \frac{3x+1}{x^2-9} }

4) In the upper fraction x+2 in the numerator cancels out with x + 2 in the denominator.

\frac{ \frac{1}{x^2-9} }{ \frac{3x+1}{x^2-9} }

5) x² - 9 in both denominators cancel out each other, and the final result is:

\frac{1}{3x+1}
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