Solve for z limit as x approaches -1 of (x^2+yx+z)/(x^2-1)=3

$lim_{x \to - 1} \frac{x^{2} + y x + z}{x^{2} - 1} = 3$

Step 1

Since the function approaches $- \infty$ from the left and $\infty$ from the right, the limit does not exist.

$Does not exist = 3$

Step 2

Move all terms not containing $D$ to the right side of the equation.

Subtract $lim_{x \to - 1} \frac{x^{2} + y x + z}{x^{2} - 1}$ from both sides of the equation.

$0 = 3 - lim_{x \to - 1} \frac{x^{2} + y x + z}{x^{2} - 1}$

Since the function approaches $- \infty$ from the left and $\infty$ from the right, the limit does not exist.

$0 = 3 - Does not exist$

Reorder factors in $3 - Does not exist$ .

$0 = 3 - lim_{x \to - 1} \frac{x^{2} + y x + z}{x^{2} - 1}$

Step 3

Rewrite the equation as $3 - lim_{x \to - 1} \frac{x^{2} + y x + z}{x^{2} - 1} = 0$ .

$3 - lim_{x \to - 1} \frac{x^{2} + y x + z}{x^{2} - 1} = 0$