Solve sqrt{2016}=quad=2n-3/n-1

$$\sqrt { 2016 } = \quad = \frac { 2 n - 3 } { n - 1 }$$

Solve for n

$$n=-\frac{3\sqrt{14}}{503}+\frac{1005}{1006}\approx 0.976689916$$

Steps for Solving Linear Equation

Variable n cannot be equal to 1 since division by zero is not defined. Multiply both sides of the equation by n-1.

$$\left(n-1\right)\sqrt{2016}=2n-3$$

Factor 2016=12^{2}\times 14. Rewrite the square root of the product \sqrt{12^{2}\times 14} as the product of square roots \sqrt{12^{2}}\sqrt{14}. Take the square root of 12^{2}.

$$\left(n-1\right)\times 12\sqrt{14}=2n-3$$

Use the distributive property to multiply n-1 by 12.

$$\left(12n-12\right)\sqrt{14}=2n-3$$

Use the distributive property to multiply 12n-12 by \sqrt{14}.

$$12n\sqrt{14}-12\sqrt{14}=2n-3$$

Subtract 2n from both sides.

$$12n\sqrt{14}-12\sqrt{14}-2n=-3$$

Add 12\sqrt{14} to both sides.

$$12n\sqrt{14}-2n=-3+12\sqrt{14}$$

Combine all terms containing n.

$$\left(12\sqrt{14}-2\right)n=-3+12\sqrt{14}$$

The equation is in standard form.

$$\left(12\sqrt{14}-2\right)n=12\sqrt{14}-3$$

Divide both sides by 12\sqrt{14}-2.

$$\frac{\left(12\sqrt{14}-2\right)n}{12\sqrt{14}-2}=\frac{12\sqrt{14}-3}{12\sqrt{14}-2}$$

Dividing by 12\sqrt{14}-2 undoes the multiplication by 12\sqrt{14}-2.

$$n=\frac{12\sqrt{14}-3}{12\sqrt{14}-2}$$

Divide -3+12\sqrt{14} by 12\sqrt{14}-2.

$$n=-\frac{3\sqrt{14}}{503}+\frac{1005}{1006}$$