Question
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Answer
The simplified form of the expression is \(-\frac{3}{29}\).
Solution
Step 1: Calculate 4².
4² = 16
Step 2: Substitute into the numerator.
10 - 16 = -6
Step 3: Calculate 7² and 3².
7² = 49; 3² = 9
Step 4: Substitute into the denominator.
49 + 9 = 58
Step 5: The expression now is:
-6/58
Step 6: Simplify by dividing numerator and denominator by 2.
-6 ÷ 2 = -3
58 ÷ 2 = 29
Final Answer: -3/29
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Simplify this solution Extra Insights
First, let’s simplify the expression step by step. First, calculate \(4^{2}\) and \(7^{2}\) and \(3^{2}\): \[ 4^{2} = 16, \quad 7^{2} = 49, \quad 3^{2} = 9. \] Now, substitute these values back into the expression: \[ \frac{10 - 16}{49 + 9}. \] This simplifies to: \[ \frac{10 - 16}{49 + 9} = \frac{-6}{58}. \] Now, we can further simplify \(\frac{-6}{58}\) by finding the greatest common divisor, which is 2: \[ \frac{-6 \div 2}{58 \div 2} = \frac{-3}{29}. \] Thus, the simplified form of the expression is: \[ \frac{-3}{29}. \]
