Question
divide these fractions and simplify the answer.
3x/16 divided by 3x-9/20
3x/16 divided by 3x-9/20
Answers
Answered by
GPT-4o mini
To divide the fractions \( \frac{3x}{16} \) by \( \frac{3x-9}{20} \), you can multiply by the reciprocal of the second fraction.
This means:
\[
\frac{3x}{16} \div \frac{3x - 9}{20} = \frac{3x}{16} \times \frac{20}{3x - 9}
\]
Now, we can multiply the fractions:
\[
\frac{3x \cdot 20}{16 \cdot (3x - 9)} = \frac{60x}{16(3x - 9)}
\]
Next, we simplify this expression.
1. Simplify \( 60x \) and \( 16 \):
\[
\frac{60x}{16(3x - 9)} = \frac{15x}{4(3x - 9)}
\]
2. Factor \( 3x - 9 \) in the denominator:
\[
3x - 9 = 3(x - 3)
\]
Substituting this back, we have:
\[
\frac{15x}{4 \cdot 3(x - 3)} = \frac{15x}{12(x - 3)}
\]
3. Now, simplify \( \frac{15x}{12(x - 3)} \):
\[
\frac{15x}{12(x - 3)} = \frac{5x}{4(x - 3)}
\]
Thus, the simplified answer is:
\[
\frac{5x}{4(x - 3)}
\]
This means:
\[
\frac{3x}{16} \div \frac{3x - 9}{20} = \frac{3x}{16} \times \frac{20}{3x - 9}
\]
Now, we can multiply the fractions:
\[
\frac{3x \cdot 20}{16 \cdot (3x - 9)} = \frac{60x}{16(3x - 9)}
\]
Next, we simplify this expression.
1. Simplify \( 60x \) and \( 16 \):
\[
\frac{60x}{16(3x - 9)} = \frac{15x}{4(3x - 9)}
\]
2. Factor \( 3x - 9 \) in the denominator:
\[
3x - 9 = 3(x - 3)
\]
Substituting this back, we have:
\[
\frac{15x}{4 \cdot 3(x - 3)} = \frac{15x}{12(x - 3)}
\]
3. Now, simplify \( \frac{15x}{12(x - 3)} \):
\[
\frac{15x}{12(x - 3)} = \frac{5x}{4(x - 3)}
\]
Thus, the simplified answer is:
\[
\frac{5x}{4(x - 3)}
\]
Answer
the real answer is 5x/4x-12
Answered by
GPT-4o mini
Let's go through the calculation step by step again to clarify the division of the fractions and ensure that we get the correct simplified form.
**Problem Statement:**
You have:
\[
\frac{3x}{16} \div \frac{3x - 9}{20}
\]
**Step 1: Convert the division into multiplication by the reciprocal.**
\[
\frac{3x}{16} \div \frac{3x - 9}{20} = \frac{3x}{16} \times \frac{20}{3x - 9}
\]
**Step 2: Multiply the fractions.**
\[
= \frac{3x \cdot 20}{16 \cdot (3x - 9)} = \frac{60x}{16(3x - 9)}
\]
**Step 3: Simplify the expression.**
First, let's simplify the numerator and the denominator:
1. Factor \(3x - 9\):
\[
3x - 9 = 3(x - 3)
\]
2. Substitute this factor into the expression:
\[
= \frac{60x}{16 \cdot 3(x - 3)} = \frac{60x}{48(x - 3)}
\]
3. Now simplify \( \frac{60x}{48(x - 3)} \):
\[
= \frac{5x}{4(x - 3)}
\]
**Final Result:**
Thus, the correct simplified expression is:
\[
\frac{5x}{4(x - 3)}
\]
**Alternative Representation:**
Alternatively, if you want to represent it differently, you can express \(4(x - 3)\) as \(4x - 12\), leading to:
\[
\frac{5x}{4(x - 3)} = \frac{5x}{4x - 12}
\]
Therefore, both forms \(\frac{5x}{4(x - 3)}\) and \(\frac{5x}{4x - 12}\) are equivalent.
Thank you for your patience, and I hope this clears up any confusion!
**Problem Statement:**
You have:
\[
\frac{3x}{16} \div \frac{3x - 9}{20}
\]
**Step 1: Convert the division into multiplication by the reciprocal.**
\[
\frac{3x}{16} \div \frac{3x - 9}{20} = \frac{3x}{16} \times \frac{20}{3x - 9}
\]
**Step 2: Multiply the fractions.**
\[
= \frac{3x \cdot 20}{16 \cdot (3x - 9)} = \frac{60x}{16(3x - 9)}
\]
**Step 3: Simplify the expression.**
First, let's simplify the numerator and the denominator:
1. Factor \(3x - 9\):
\[
3x - 9 = 3(x - 3)
\]
2. Substitute this factor into the expression:
\[
= \frac{60x}{16 \cdot 3(x - 3)} = \frac{60x}{48(x - 3)}
\]
3. Now simplify \( \frac{60x}{48(x - 3)} \):
\[
= \frac{5x}{4(x - 3)}
\]
**Final Result:**
Thus, the correct simplified expression is:
\[
\frac{5x}{4(x - 3)}
\]
**Alternative Representation:**
Alternatively, if you want to represent it differently, you can express \(4(x - 3)\) as \(4x - 12\), leading to:
\[
\frac{5x}{4(x - 3)} = \frac{5x}{4x - 12}
\]
Therefore, both forms \(\frac{5x}{4(x - 3)}\) and \(\frac{5x}{4x - 12}\) are equivalent.
Thank you for your patience, and I hope this clears up any confusion!