Question
ombine the following fractions and express in fully reduced forn \[ \frac{9 x}{2}-\frac{2 x}{9} \]
Ask by Jimenez Sherman. in the United States
Feb 19,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The simplified form is \(\frac{77x}{18}\).
Solution
Calculate or simplify the expression \( \frac{9x}{2}-\frac{2x}{9} \).
Simplify the expression by following steps:
- step0: Solution:
\(\frac{9x}{2}-\frac{2x}{9}\)
- step1: Reduce fractions to a common denominator:
\(\frac{9x\times 9}{2\times 9}-\frac{2x\times 2}{9\times 2}\)
- step2: Multiply the numbers:
\(\frac{9x\times 9}{18}-\frac{2x\times 2}{9\times 2}\)
- step3: Multiply the numbers:
\(\frac{9x\times 9}{18}-\frac{2x\times 2}{18}\)
- step4: Transform the expression:
\(\frac{9x\times 9-2x\times 2}{18}\)
- step5: Multiply the terms:
\(\frac{81x-2x\times 2}{18}\)
- step6: Multiply the terms:
\(\frac{81x-4x}{18}\)
- step7: Subtract the terms:
\(\frac{77x}{18}\)
The fully reduced form of the expression \(\frac{9x}{2}-\frac{2x}{9}\) is \(\frac{77x}{18}\).
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Simplify this solution Extra Insights
To combine the fractions \(\frac{9x}{2}\) and \(-\frac{2x}{9}\), we first need to find a common denominator. The least common multiple of 2 and 9 is 18. Now we can rewrite each fraction: \[ \frac{9x}{2} = \frac{9x \cdot 9}{2 \cdot 9} = \frac{81x}{18} \] \[ -\frac{2x}{9} = -\frac{2x \cdot 2}{9 \cdot 2} = -\frac{4x}{18} \] Now, we can combine the fractions: \[ \frac{81x}{18} - \frac{4x}{18} = \frac{81x - 4x}{18} = \frac{77x}{18} \] The final expression is \(\frac{77x}{18}\), which is already in its simplest form.
