Reduce the following rational expression to the lowest terms. When is this undefined? How did you determine when it was undefined?

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asked Aug 10, 2023 145k views

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Reduce the following rational expression to the lowest terms. When is this undefined? How did you determine when it was undefined?

Reduce the following rational expression to the lowest terms. When is this undefined-example-1

Mathematics
college

Elza asked

by Elza

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$\begin{gathered} (6x^2+7x-3)/(4x^2-9) \\ 6x^2+7x-3=(2x+3)(3x-1) \\ 4x^2-9=(2x+3)(2x-3) \\ (6x^2+7x-3)/(4x^2-9)=((2x+3)(3x-1))/((2x+3)(2x-3))=(3x-1)/(2x-3) \\ (6x^2+7x-3)/(4x^2-9)=(3x-1)/(2x-3) \\ \text{The expression }(6x^2+7x-3)/(4x^2-9)\text{ in lowest terms is }(3x-1)/(2x-3) \\ To\text{ determine when is undefined} \\ 2x-3=0 \\ 2x=3 \\ x=(3)/(2) \\ The\text{ expression is undefined when x is }(3)/(2) \end{gathered}$