Which of the following is the quotient of the rational expressions shown below?๐ฅ+22๐ฅ+72x+7x+2โ รทรท ๐ฅ4๐ฅโ2xโ2x 4 โ A.โ๐ฅ42๐ฅ+72x+7โx 4 โ B.๐ฅ2โ42๐ฅ5+7๐ฅ42x 5 +7x 4 x 2 โ4โ C.๐ฅ4+๐ฅ+23๐ฅ+53x+5x 4 +x+2โ D.๐ฅ5+2๐ฅ42๐ฅ2+3๐ฅโ142x 2 +3xโ14x 5 +2x 4 โ SUBMITarrow_backPREVIOUS
Question
Which of the following is the quotient of the rational expressions shown below?๐ฅ+22๐ฅ+72x+7x+2โ รทรท ๐ฅ4๐ฅโ2xโ2x 4 โ A.โ๐ฅ42๐ฅ+72x+7โx 4 โ B.๐ฅ2โ42๐ฅ5+7๐ฅ42x 5 +7x 4 x 2 โ4โ C.๐ฅ4+๐ฅ+23๐ฅ+53x+5x 4 +x+2โ D.๐ฅ5+2๐ฅ42๐ฅ2+3๐ฅโ142x 2 +3xโ14x 5 +2x 4 โ SUBMITarrow_backPREVIOUS
Solution
The question seems to be a bit jumbled, but I'll try to interpret it as best as I can.
You're asked to find the quotient of two rational expressions. The first expression is (x+2)/(x+7) and the second expression is (x-2)/(x+4).
When you divide two fractions, you multiply the first fraction by the reciprocal of the second fraction.
So, the division problem (x+2)/(x+7) รท (x-2)/(x+4) becomes (x+2)/(x+7) * (x+4)/(x-2).
Now, you just multiply across.
The numerator becomes (x+2)(x+4) and the denominator becomes (x+7)(x-2).
So, the quotient of the rational expressions is ((x+2)(x+4))/((x+7)(x-2)).
This doesn't seem to match any of the answer choices you provided, so there might have been a mistake in the question or the answer choices.
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