What is the limit as x approaches 2/3 of (2x^2-15x+18)/(3x^2-17x-6) ?

The limit as x approaches 2/3 of (2x^2-15x+18)/(3x^2-17x-6) is -5/9

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limit as x approaches 2/3 of (2x^2-15x+18)/(3x^2-17x-6)

x \to \frac{2}{3} lim (\frac{2 x ^{2} - 15 x + 18}{3 x ^{2} - 17 x - 6})

- \frac{5}{9}

Decimal Notation

- 0.55555 \dots

Solution steps

x \to \frac{2}{3} lim (\frac{2 x ^{2} - 15 x + 18}{3 x ^{2} - 17 x - 6})

Plug in the value

x = \frac{2}{3}

= \frac{2 ( \frac{2}{3} ) ^{2} - 15 \cdot \frac{2}{3} + 18}{3 ( \frac{2}{3} ) ^{2} - 17 \cdot \frac{2}{3} - 6}

Simplify

\frac{2 ( \frac{2}{3} ) ^{2} - 15 \cdot \frac{2}{3} + 18}{3 ( \frac{2}{3} ) ^{2} - 17 \cdot \frac{2}{3} - 6} : - \frac{5}{9}

= - \frac{5}{9}

x \to 2 + lim (\frac{2 - 4 x}{x - 2})

x \to 1 + lim (\frac{∣ 1 - x ∣}{x - 1})

x \to 5 lim (17 - x)

x \to 5 lim (\frac{x}{10 - 2 x})

x \to \frac{2}{3} + lim (3 x - 2)

What is the limit as x approaches 2/3 of (2x^2-15x+18)/(3x^2-17x-6) ?
The limit as x approaches 2/3 of (2x^2-15x+18)/(3x^2-17x-6) is -5/9