Find the excluded value of the fraction. \frac{x + 11}{3x^2 + 5x - 2}

Question:

Find the excluded value of the fraction.

{eq}\displaystyle \frac{x + 11}{3x^2 + 5x - 2} {/eq}

Excluded Value:

If an expression is not defined at a value of the variable then it is called the excluded value of the expression. For example, a fraction is not defined when its denominator is zero. So the excluded value of the fraction {eq}\dfrac{1}{x} {/eq} is {eq}x=0 {/eq}.

Answer and Explanation:

The given function is:

$$\displaystyle \frac{x + 11}{3x^2 + 5x - 2} $$

We know that a fraction is not defined when its denominator is zero.

So, to find excluded values of x, we will set the denominator to be zero.

$$3x^2 + 5x - 2 =0 $$

Here, {eq}3(-2)=-6 {/eq} and the middle term is, {eq}5 {/eq}.

So, we have to find two numbers whose product is -6 and whose sum is 5.

Two such numbers are 6 and -1.

So, the above equation becomes:

$$3x^2 +6x-1x-2=0 \\ 3x(x+2)-1(x+2)=0 \\ (x+2)(3x-1)=0 \\ x+2=0; \,\, 3x-1=0 \\ \boxed{\mathbf{x=-2; \,\, x = \dfrac{1}{3}}} $$


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Expressions of Rational Functions

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