Q5. - Algebra 1

Question

State whether each sentence is true or false. If false, replace the underlined word, phrase, expression, or number to make a true sentence.

 

The excluded values for $\frac{x}{x^2+5x+6}$ are -2 and -3.

Step-by-Step Solution

Answer

The given statement is True.

Step 1. State the concept.

A rational expression is an algebraic expression whose numerator and denominator are polynomials. Also, division by 0 is undefined, so therefore, the polynomials in the denominator cannot be zero and the values for which the denominator is zero is termed as excluded values for the respective rational expression.

Step 2. Explanation of the statement.

Factor the denominator in $\frac{x}{x^2+5x+6}$, to find out the excluded values.

$$\begin{gathered} x^2+5x+6=0 \\ {x}^2+3x+2x+6=0 \\ \left(x+3\right)\left(x+2\right)=0 \\ x=-3,-2 \end{gathered}$$

Step 3. Write whether the statement is true or false.

Since, $x=-3,-2$, therefore, given statement is “The excluded values for $\frac{x}{x^2+5x+6}$ are -2 and -3.” is true.