Solve v/1-sqrt{11}=v

$$\frac { v } { 1 - \sqrt { 11 } } = v$$

Solve for v

$$v=0$$

Steps for Solving Linear Equation

Rationalize the denominator of \frac{v}{1-\sqrt{11}} by multiplying numerator and denominator by 1+\sqrt{11}.

$$\frac{v\left(1+\sqrt{11}\right)}{\left(1-\sqrt{11}\right)\left(1+\sqrt{11}\right)}=v$$

Consider \left(1-\sqrt{11}\right)\left(1+\sqrt{11}\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{v\left(1+\sqrt{11}\right)}{1^{2}-\left(\sqrt{11}\right)^{2}}=v$$

Square 1. Square \sqrt{11}.

$$\frac{v\left(1+\sqrt{11}\right)}{1-11}=v$$

Subtract 11 from 1 to get -10.

$$\frac{v\left(1+\sqrt{11}\right)}{-10}=v$$

Use the distributive property to multiply v by 1+\sqrt{11}.

$$\frac{v+v\sqrt{11}}{-10}=v$$

Subtract v from both sides.

$$\frac{v+v\sqrt{11}}{-10}-v=0$$

Multiply both sides of the equation by -10.

$$v+v\sqrt{11}+10v=0$$

Reorder the terms.

$$\sqrt{11}v+v+10v=0$$

Combine v and 10v to get 11v.

$$\sqrt{11}v+11v=0$$

Combine all terms containing v.

$$\left(\sqrt{11}+11\right)v=0$$

Divide 0 by \sqrt{11}+11.

$$v=0$$