What is the limit as x approaches 6 of (x^2+11x-30)/(x^2-13x-42) ?

The limit as x approaches 6 of (x^2+11x-30)/(x^2-13x-42) is -6/7

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limit as x approaches 6 of (x^2+11x-30)/(x^2-13x-42)

x \to 6 lim (\frac{x ^{2} + 11 x - 30}{x ^{2} - 13 x - 42})

- \frac{6}{7}

Decimal

- 0.85714 \dots

Solution steps

x \to 6 lim (\frac{x ^{2} + 11 x - 30}{x ^{2} - 13 x - 42})

Plug in the value

x = 6

= \frac{6 ^{2} + 11 \cdot 6 - 30}{6 ^{2} - 13 \cdot 6 - 42}

Simplify

\frac{6 ^{2} + 11 \cdot 6 - 30}{6 ^{2} - 13 \cdot 6 - 42} : - \frac{6}{7}

= - \frac{6}{7}

What is the limit as x approaches 6 of (x^2+11x-30)/(x^2-13x-42) ?
The limit as x approaches 6 of (x^2+11x-30)/(x^2-13x-42) is -6/7