To add the fractions with different denominators, we need to find a common denominator:
4. For \(x\), the common denominator between 3 and 7 is \(3 \times 7 = 21\). So, \( \frac{1}{3} + \frac{2}{7} = \frac{7}{21} + \frac{6}{21} = \frac{13}{21} \).
5. The expression now becomes: \( \frac{13}{21}x - \frac{4}{3}y \)
Therefore, the simplified expression is \( \frac{13}{21}x - \frac{4}{3}y \).
Answers & Comments
Given :
[tex] = \frac{1}{3x} + \frac{2}{5y} \times \frac{5}{7x} - \frac{4}{3y} \\ [/tex]
Solution Explanation :
[tex]= \frac{1}{3x} + \frac{2}{5y} \times \frac{5}{7x} - \frac{4}{3y} \\ \\ = ( \frac{1}{3x} + \frac{2}{5y} ) \times (\frac{5}{7x} - \frac{4}{3y}) \\ \\ = ( \frac{5y + 6x}{15xy} ) \times ( \frac{15y - 28x}{21xy} ) \\ \\ = \frac{75y - 168y}{315xy} [/tex]
Answer:
The expression you've provided is \( \frac{1}{3}x + \frac{2}{5}y \times \frac{5}{7}x - \frac{4}{3}y \).
To simplify this expression, let's break it down step by step:
1. \( \frac{1}{3}x + \frac{2}{5}y \times \frac{5}{7}x - \frac{4}{3}y \)
First, simplify the multiplication within the expression:
2. \( \frac{1}{3}x + \frac{2}{7}x - \frac{4}{3}y \)
Now, combine the terms with \(x\) and the terms with \(y\):
3. \( \left(\frac{1}{3} + \frac{2}{7}\right)x - \frac{4}{3}y \)
To add the fractions with different denominators, we need to find a common denominator:
4. For \(x\), the common denominator between 3 and 7 is \(3 \times 7 = 21\). So, \( \frac{1}{3} + \frac{2}{7} = \frac{7}{21} + \frac{6}{21} = \frac{13}{21} \).
5. The expression now becomes: \( \frac{13}{21}x - \frac{4}{3}y \)
Therefore, the simplified expression is \( \frac{13}{21}x - \frac{4}{3}y \).
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