What is the limit as x approaches 3/4 of (4x^2-9)/(2x-3) ?

The limit as x approaches 3/4 of (4x^2-9)/(2x-3) is 9/2

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limit as x approaches 3/4 of (4x^2-9)/(2x-3)

x \to \frac{3}{4} lim (\frac{4 x ^{2} - 9}{2 x - 3})

\frac{9}{2}

Solution steps

x \to \frac{3}{4} lim (\frac{4 x ^{2} - 9}{2 x - 3})

Plug in the value

x = \frac{3}{4}

= \frac{4 ( \frac{3}{4} ) ^{2} - 9}{2 \cdot \frac{3}{4} - 3}

Simplify

\frac{4 ( \frac{3}{4} ) ^{2} - 9}{2 \cdot \frac{3}{4} - 3} : \frac{9}{2}

= \frac{9}{2}

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What is the limit as x approaches 3/4 of (4x^2-9)/(2x-3) ?
The limit as x approaches 3/4 of (4x^2-9)/(2x-3) is 9/2