Simplify the expression completely if possible. (3x^2-3x)/(x^2)-5x-6 Answer Attemptiout of 3 square

To simplify the expression \(\frac{3x^2 - 3x}{x^2 - 5x - 6}\), we need to factor both the numerator and the denominator.<br /><br />First, let's factor the numerator:<br />\[ 3x^2 - 3x \]<br />We can factor out a common factor of 3:<br />\[ 3x(x - 1) \]<br /><br />Next, let's factor the denominator:<br />\[ x^2 - 5x - 6 \]<br />We need to find two numbers that multiply to \(-6\) and add up to \(-5\). These numbers are \(-6\) and \(1\):<br />\[ x^2 - 5x - 6 = (x - 6)(x + 1) \]<br /><br />Now we can rewrite the original expression with these factored forms:<br />\[ \frac{3x(x - 1)}{(x - 6)(x + 1)} \]<br /><br />Since there are no common factors in the numerator and the denominator that can be canceled out, this is the simplified form of the expression:<br />\[ \boxed{\frac{3x(x - 1)}{(x - 6)(x + 1)}} \]