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zmey [24]
3 years ago
15

Given the rational expressions 7/(x ^ 2 - 12) and (2x - 1)/(x + 2) which of the following is true?

Mathematics
1 answer:
goldenfox [79]3 years ago
3 0

Answer:

option C

Step-by-step explanation:

\frac{\frac{2x-1}{x+2}}{\frac{7}{x^{2}-12}}=\frac{2x-1}{x+2}*\frac{x^{2}-12}{7}\\\\\\=\frac{(2x-1)(x^{2}-12)}{7(x+2)}

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Reduce each ratio to its minimum expression to find if they are equal.

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\begin{gathered} \frac{10}{8}=\frac{2\cdot5}{2\cdot4} \\ =\frac{5}{4} \end{gathered}

Since both ratios reduce to 5:4, they are equivalent.

Another way to check a:b is equivalent to c:d, is that a*d = b*c

In this case, this will be true if 35 times 8 is equal to 10 times 28:

\begin{gathered} 35\cdot8=280 \\ 10\cdot28=280 \end{gathered}

Since both products are equal, then the ratios are equivalent.

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