Simplify: [tex]$\frac{3}{7 x}+\frac{4}{5 x^2}$[/tex]
Answer (2)
To simplify the expression, we find a common denominator and combine the fractions. The simplified expression is 35 x 2 15 x + 28 .
Explanation
Understanding the Problem We are given the expression 7 x 3 + 5 x 2 4 to simplify.
Objective The objective is to combine these two fractions into a single fraction.
Common Denominator We need to find a common denominator to add these fractions.
Identifying Components The common denominator will involve both x and x 2 , as well as the constants 7 and 5.
Examples
Fractions are a fundamental concept in mathematics and have numerous real-world applications. For instance, when baking, you often need to combine different amounts of ingredients, which can be expressed as fractions. Simplifying these fractions helps in accurately measuring and combining the ingredients to achieve the desired outcome. Similarly, in construction or engineering, combining different materials or forces often involves adding fractions to ensure structural integrity and stability.
To simplify the expression 7 x 3 + 5 x 2 4 , we find the least common denominator, which is 35 x 2 . By rewriting each fraction with this common denominator, we combine them to get 35 x 2 15 x + 28 as the final result.
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