Question

Divide. Write the answer in lowest terms.StartFraction 2 minus j Over 15 EndFraction divided by StartFraction j minus 2 Over 21 EndFraction
equals
  
enter your response here
​(Simplify your answer. Use integers or fractions for any numbers in the​ expression.)

Answer 1

To divide the two fractions given, we can use the rule that states that dividing by a fraction is the same as multiplying by its reciprocal. Therefore, we have:

\[
\frac{2 - j}{15} \div \frac{j - 2}{21} = \frac{2 - j}{15} \times \frac{21}{j - 2}
\]

Next, we can simplify this expression. We notice that \(j - 2\) is the same as \(-(2 - j)\). Therefore:

\[
\frac{21}{j - 2} = \frac{21}{-(2 - j)} = -\frac{21}{2 - j}
\]

Substituting this back into our expression gives:

\[
\frac{2 - j}{15} \times -\frac{21}{2 - j}
\]

The \(2 - j\) terms cancel out:

\[
-\frac{21}{15}
\]

Now, we simplify \(-\frac{21}{15}\). The greatest common divisor (GCD) of 21 and 15 is 3:

\[
-\frac{21 \div 3}{15 \div 3} = -\frac{7}{5}
\]

Thus, the final answer in lowest terms is:

\[
\boxed{-\frac{7}{5}}
\]