For what positive integer value of x is the rational expression \frac{2x - 5}{3x^2 - 10x -… — ACT

For what positive integer value of $x$ is the rational expression $\frac{2x - 5}{3x^2 - 10x - 8}$ undefined?

Answer:The expression is undefined when

x

is equal to 【4】.

The expression is undefined when the positive integer x is equal to 4.

The rational expression is undefined when its denominator is 0. Setting the denominator

3x^2 - 10x - 8

equal to 0 and factoring gives

(3x + 2)(x - 4) = 0

. The roots of this equation are

x = -\frac{2}{3}

and

x = 4

. Since the question restricts the target value to a positive integer, the correct value is 4.

Set the denominator of the rational expression equal to 0.

3x^2 - 10x - 8 = 0

A rational expression is undefined when its denominator is equal to 0 because division by zero is undefined.

Factor the quadratic equation

3x^2 - 10x - 8 = 0

(3x + 2)(x - 4) = 0

Factoring the quadratic trinomial helps identify the values of x that satisfy the equation.

Solve for the roots by setting each factor to 0.

x = -\frac{2}{3}

x = 4

According to the zero product property, if the product of two factors is zero, then at least one of the factors must be zero.

Filter the solutions based on the given constraint.

x = 4

The question specifies that x must be a positive integer. Since

-\frac{2}{3}

is a negative fraction, we reject it and select 4.

Finding values that make a rational expression undefined by setting the denominator to zero and solving the resulting quadratic equation.

Estimated Time:1m 30s

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