Question

For what values of the variable is the rational expression undefined? $$\frac{x-3}{x^{2}+5 x-6}$$

Short answer

The values of x that make the rational expression undefined are x=-6 and x=1

Step-by-step solution

Identify the Denominator of the Rational Expression

The denominator of the given rational expression is \(x^{2}+5x-6\)

Set the Denominator Equal to Zero

To find the values of x that make the expression undefined, set the denominator equal to zero: \(x^{2}+5x-6=0\)

Solve the Equation

To solve the quadratic equation, we can use factoring. The quadratic \(x^{2}+5x-6\) can be factored into \((x+6)(x-1)=0\)

Solve for X

Setting each factor equal to zero gives the solutions, x=-6 and x=1