For what values of y is the expression \(\frac{6y-1}{y^2 - y-6}\)

For what values of y is the expression \(\frac{6y-1}{y^2 - y-6}\)

Answer Details

To determine the values of y for which the expression \(\frac{6y-1}{y^2 - y-6}\) is defined, we need to find the values of y that make the denominator of the expression nonzero. The denominator of the expression is \(y^2 - y-6\), which can be factored as \((y-3)(y+2)\). Therefore, the expression is undefined when \(y=3\) or \(y=-2\), because in those cases the denominator becomes zero. So, the values of y for which the expression is defined are all the real numbers except 3 and -2. That means, y can be any number other than 3 and -2. Therefore, the correct answer is: y can be any number other than 3 and -2.