Find the value of the expression when [tex]y =-2[/tex].
[tex]\frac{y^3}{y^2-1}[/tex]
Answer (1)
Substitute y = − 2 into the expression y 2 − 1 y 3 .
Evaluate the numerator: ( − 2 ) 3 = − 8 .
Evaluate the denominator: ( − 2 ) 2 − 1 = 3 .
Simplify the expression: 3 − 8 . The final answer is − 3 8 .
Explanation
Understanding the problem We are given the expression y 2 − 1 y 3 and asked to find its value when y = − 2 .
Substitution Substitute y = − 2 into the expression: y 2 − 1 y 3 = ( − 2 ) 2 − 1 ( − 2 ) 3
Evaluating the numerator Evaluate the numerator: ( − 2 ) 3 = − 8
Evaluating the denominator Evaluate the denominator: ( − 2 ) 2 − 1 = 4 − 1 = 3
Simplifying the expression So the expression becomes: 3 − 8 = − 3 8
Final Answer Therefore, the value of the expression when y = − 2 is − 3 8 .
Examples
Imagine you are designing a bridge and need to calculate the stress on a particular support beam. The expression y 2 − 1 y 3 could represent a simplified model of that stress, where 'y' is a factor related to the load. By substituting different values of 'y', you can analyze how the stress changes under varying conditions. This type of calculation is crucial in ensuring the structural integrity and safety of the bridge.
