Solve 2/n-3=3/x-2

$$\frac { 2 } { n - 3 } = \frac { 3 } { x - 2 }$$

Solve for n

$$n=\frac{2x+5}{3}$$

$$x\neq 2$$

Steps for Solving Linear Equation

Variable n cannot be equal to 3 since division by zero is not defined. Multiply both sides of the equation by \left(n-3\right)\left(x-2\right), the least common multiple of n-3,x-2.

$$\left(x-2\right)\times 2=\left(n-3\right)\times 3$$

Use the distributive property to multiply x-2 by 2.

$$2x-4=\left(n-3\right)\times 3$$

Use the distributive property to multiply n-3 by 3.

$$2x-4=3n-9$$

Swap sides so that all variable terms are on the left hand side.

$$3n-9=2x-4$$

Add 9 to both sides.

$$3n=2x-4+9$$

Add -4 and 9 to get 5.

$$3n=2x+5$$

Divide both sides by 3.

$$\frac{3n}{3}=\frac{2x+5}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$n=\frac{2x+5}{3}$$

Variable n cannot be equal to 3.

$$n=\frac{2x+5}{3}\text{, }n\neq 3$$

Solve for x

$$x=\frac{3n-5}{2}$$

$$n\neq 3$$

Steps for Solving Linear Equation

Variable x cannot be equal to 2 since division by zero is not defined. Multiply both sides of the equation by \left(n-3\right)\left(x-2\right), the least common multiple of n-3,x-2.

$$\left(x-2\right)\times 2=\left(n-3\right)\times 3$$

Use the distributive property to multiply x-2 by 2.

$$2x-4=\left(n-3\right)\times 3$$

Use the distributive property to multiply n-3 by 3.

$$2x-4=3n-9$$

Add 4 to both sides.

$$2x=3n-9+4$$

Add -9 and 4 to get -5.

$$2x=3n-5$$

Divide both sides by 2.

$$\frac{2x}{2}=\frac{3n-5}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$x=\frac{3n-5}{2}$$

Variable x cannot be equal to 2.

$$x=\frac{3n-5}{2}\text{, }x\neq 2$$