What is the limit as x approaches 3 of (x^2-9)/(x^2-10x+21) ?

The limit as x approaches 3 of (x^2-9)/(x^2-10x+21) is -3/2

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limit as x approaches 3 of (x^2-9)/(x^2-10x+21)

x \to 3 lim (\frac{x ^{2} - 9}{x ^{2} - 10 x + 21})

- \frac{3}{2}

Decimal

- 1.5

Solution steps

x \to 3 lim (\frac{x ^{2} - 9}{x ^{2} - 10 x + 21})

Simplify

\frac{x ^{2} - 9}{x ^{2} - 10 x + 21} : \frac{x + 3}{x - 7}

= x \to 3 lim (\frac{x + 3}{x - 7})

Plug in the value

x = 3

= \frac{3 + 3}{3 - 7}

Simplify

\frac{3 + 3}{3 - 7} : - \frac{3}{2}

= - \frac{3}{2}

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What is the limit as x approaches 3 of (x^2-9)/(x^2-10x+21) ?
The limit as x approaches 3 of (x^2-9)/(x^2-10x+21) is -3/2