Calculus Examples

$\frac{lim_{x \to - 5} 3 x}{2 x + 10}$

Step 1

Move the term $3$ outside of the limit because it is constant with respect to $x$ .

$\frac{3 lim_{x \to - 5} x}{2 x + 10}$

Step 2

Evaluate the limit of $x$ by plugging in $- 5$ for $x$ .

$\frac{3 \cdot - 5}{2 x + 10}$

Step 3

Simplify the answer.

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Step 3.1

Multiply $3$ by $- 5$ .

$\frac{- 15}{2 x + 10}$

Step 3.2

Factor $2$ out of $2 x + 10$ .

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Step 3.2.1

Factor $2$ out of $2 x$ .

$\frac{- 15}{2 (x) + 10}$

Step 3.2.2

Factor $2$ out of $10$ .

$\frac{- 15}{2 x + 2 \cdot 5}$

Step 3.2.3

Factor $2$ out of $2 x + 2 \cdot 5$ .

$\frac{- 15}{2 (x + 5)}$

Step 3.3

Move the negative in front of the fraction.

$- \frac{15}{2 (x + 5)}$