To divide the fractions and then simplify, follow these steps:
1. **Identify the fractions**: We have \(\frac{7}{x-5}\) divided by \(\frac{12}{2x-10}\).
2. **Rewrite the division as multiplication**: Invert the second fraction (\(\frac{12}{2x-10}\)) and then multiply:
\[
\frac{7}{x-5} \div \frac{12}{2x-10} = \frac{7}{x-5} \times \frac{2x-10}{12}
\]
3. **Simplify the second fraction**: Notice that \(2x - 10\) can be factored as \(2(x - 5)\). Therefore, the second fraction becomes:
\[
\frac{2(x-5)}{12}
\]
4. **Multiply the fractions**: Now we have:
\[
\frac{7}{x-5} \times \frac{2(x-5)}{12}
\]
5. **Cancel out common factors**: The factor \(x-5\) appears in both the numerator and the denominator and can be canceled out:
\[
\frac{7}{x-5} \times \frac{2(x-5)}{12} = \frac{7 \times 2}{12} = \frac{14}{12}
\]
6. **Simplify the result**: The fraction \(\frac{14}{12}\) can be simplified by dividing the numerator and the denominator by their greatest common divisor (GCD), which is 2:
\[
\frac{14}{12} = \frac{14 \div 2}{12 \div 2} = \frac{7}{6}
\]
So, the simplified answer is:
\[
\frac{7}{6}
\]
divide these fractions and select the simplified answer,
7/x-5/12/2x-10
invert the bottom fraction and then multiply normally.
1 answer