Simplify $\frac{15 m^2+7 m^2-4 m^2}{9 m^2-3 m^2}$
Answer (2)
Combine like terms in the numerator: 15 m 2 + 7 m 2 − 4 m 2 = 18 m 2 .
Combine like terms in the denominator: 9 m 2 − 3 m 2 = 6 m 2 .
Simplify the fraction: 6 m 2 18 m 2 = 6 18 .
Divide to get the final answer: 3 .
Explanation
Understanding the Problem We are asked to simplify the expression 9 m 2 − 3 m 2 15 m 2 + 7 m 2 − 4 m 2 . This involves combining like terms in both the numerator and the denominator and then simplifying the resulting fraction.
Simplifying the Numerator First, let's simplify the numerator by combining the like terms: 15 m 2 + 7 m 2 − 4 m 2 = ( 15 + 7 − 4 ) m 2 = 18 m 2
Simplifying the Denominator Next, let's simplify the denominator by combining the like terms: 9 m 2 − 3 m 2 = ( 9 − 3 ) m 2 = 6 m 2
Rewriting the Expression Now, we can rewrite the expression as: 6 m 2 18 m 2
Simplifying the Fraction Finally, we simplify the fraction by dividing both the numerator and the denominator by their greatest common factor, which includes m 2 :
6 m 2 18 m 2 = 6 18 = 3
Examples
Simplifying algebraic expressions is a fundamental skill in mathematics and has practical applications in various fields. For instance, consider a scenario where you need to calculate the total area of a garden consisting of several rectangular sections with varying dimensions. If the lengths and widths of these sections are expressed in terms of variables, simplifying the expression representing the total area can help you efficiently determine the amount of fencing required or the quantity of fertilizer needed. This skill is also crucial in physics, engineering, and computer science, where complex formulas often need to be simplified for efficient computation and analysis.
The expression 9 m 2 − 3 m 2 15 m 2 + 7 m 2 − 4 m 2 simplifies to 3 after combining like terms in both the numerator and denominator, and dividing by common factors. The final answer is 3 .
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