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Simplify. 3x−3/ x2+x−2⋅4x+8 /6x+18
a. 2/3(x+3) b. (x+3)/2 c. 2(x−1)/(x+3) d. 2/(x+3)

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Answer: To simplify the given expression, let's break it down step by step:

\[ \frac{3x - 3}{x^2 + x - 2} \cdot \frac{4x + 8}{6x + 18} \]

Factor the denominators and numerators where possible:

\[ \frac{3(x - 1)}{(x + 2)(x - 1)} \cdot \frac{4(x + 2)}{6(x + 3)} \]

Now, cancel out common factors in the numerators and denominators:

\[ \frac{3}{x + 2} \cdot \frac{4}{3} \]

Simplify the fractions and cancel common factors:

\[ \frac{4}{x + 2} \]

The simplified expression is:

\[ \frac{4}{x + 2} \]

The correct option is: d. \( \frac{4}{x + 2} \)

Explanation:

User Pritam Karmakar
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