Solve for y limit as x approaches y of (yx)/3=12

$lim_{x \to y} \frac{y x}{3} = 12$

Step 1

Simplify $lim_{x \to y} \frac{y x}{3}$ .

Move the term $\frac{y}{3}$ outside of the limit because it is constant with respect to $x$ .

$\frac{y}{3} lim_{x \to y} x = 12$

Evaluate the limit of $x$ by plugging in $y$ for $x$ .

$\frac{y}{3} y = 12$

Multiply $\frac{y}{3} y$ .

Combine $\frac{y}{3}$ and $y$ .

$\frac{y \cdot y}{3} = 12$

Raise $y$ to the power of $1$ .

$\frac{y^{1} y}{3} = 12$

Raise $y$ to the power of $1$ .

$\frac{y^{1} y^{1}}{3} = 12$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{y^{1 + 1}}{3} = 12$

Add $1$ and $1$ .

$\frac{y^{2}}{3} = 12$

Step 2

Multiply both sides of the equation by $3$ .

$3 \frac{y^{2}}{3} = 3 \cdot 12$

Step 3

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$3 \frac{y^{2}}{3} = 3 \cdot 12$

Rewrite the expression.

$y^{2} = 3 \cdot 12$

Simplify the right side.

Multiply $3$ by $12$ .

$y^{2} = 36$

Step 4

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$y = \pm \sqrt{36}$

Step 5

Simplify $\pm \sqrt{36}$ .

Rewrite $36$ as $6^{2}$ .

$y = \pm \sqrt{6^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$y = \pm 6$

Step 6

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$y = 6$

Next, use the negative value of the $\pm$ to find the second solution.

$y = - 6$

The complete solution is the result of both the positive and negative portions of the solution.

$y = 6, - 6$

Solve for y limit as x approaches y of (yx)/3=12

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