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Evaluate the expression for s=16s = -16 and t=12t = 12. Simplify your answer.\newlinets+t=\frac{t}{s} + t = ____\_\_\_\_

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Q. Evaluate the expression for s=16s = -16 and t=12t = 12. Simplify your answer.\newlinets+t=\frac{t}{s} + t = ____\_\_\_\_
  1. Identify and Substitute: Identify the expression and substitute the given values for ss and tt. Substitute s=16s = -16 and t=12t = 12 into the expression ts+t\frac{t}{s} + t. Expression: 12(16)+12\frac{12}{(-16)} + 12
  2. Simplify Fraction: Simplify the fraction 12(16)\frac{12}{(-16)}. 12(16)\frac{12}{(-16)} can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 44. Simplified fraction: 12÷4(16÷4)=3(4)\frac{12 \div 4}{(-16 \div 4)} = \frac{3}{(-4)}
  3. Add to t: Add the simplified fraction to t.\newlineNow we add 3(4)\frac{3}{(-4)} to 1212.\newlineCalculation: 3(4)+12\frac{3}{(-4)} + 12\newlineSince 1212 is the same as 121\frac{12}{1}, we can write this as:\newline3(4)+121\frac{3}{(-4)} + \frac{12}{1}
  4. Find Common Denominator: Find a common denominator to add the fractions.\newlineThe common denominator for 4-4 and 11 is 4-4.\newlineRewrite 121\frac{12}{1} with the common denominator:\newline121=12×(4)(4)=48(4)\frac{12}{1} = \frac{12 \times (-4)}{(-4)} = \frac{-48}{(-4)}\newlineNow add the two fractions:\newline3(4)+48(4)\frac{3}{(-4)} + \frac{-48}{(-4)}
  5. Perform Addition: Perform the addition of the fractions.\newlineNow that we have a common denominator, we can add the numerators:\newline(3+(48))/(4)(3 + (-48))/(-4)\newlineCalculation: (45)/(4)(-45)/(-4)
  6. Simplify Result: Simplify the result.\newlineSince both the numerator and the denominator are negative, the negatives cancel out:\newline(45)/(4)=45/4(-45)/(-4) = 45/4

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