Solve 3x+2/(x+2)*(x-1)=m/x+2+n/x-1

$$\frac { 3 x + 2 } { ( x + 2 ) \cdot ( x - 1 ) } = \frac { m } { x + 2 } + \frac { n } { x - 1 }$$

Solve for m

$$m=-\frac{2-2n+3x-nx}{1-x}$$

$$x\neq -2\text{ and }x\neq 1$$

Steps for Solving Linear Equation

Multiply both sides of the equation by \left(x-1\right)\left(x+2\right), the least common multiple of \left(x+2\right)\left(x-1\right),x+2,x-1.

$$3x+2=\left(x-1\right)m+\left(x+2\right)n$$

Use the distributive property to multiply x-1 by m.

$$3x+2=xm-m+\left(x+2\right)n$$

Use the distributive property to multiply x+2 by n.

$$3x+2=xm-m+xn+2n$$

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

$$xm-m+xn+2n=3x+2$$

Subtract xn from both sides.

$$xm-m+2n=3x+2-xn$$

Subtract 2n from both sides.

$$xm-m=3x+2-xn-2n$$

Combine all terms containing m.

$$\left(x-1\right)m=3x+2-xn-2n$$

The equation is in standard form.

$$\left(x-1\right)m=2-2n+3x-nx$$

Divide both sides by x-1.

$$\frac{\left(x-1\right)m}{x-1}=\frac{2-2n+3x-nx}{x-1}$$

Dividing by x-1 undoes the multiplication by x-1.

$$m=\frac{2-2n+3x-nx}{x-1}$$

Solve for n

$$n=\frac{2+m+3x-mx}{x+2}$$

$$x\neq -2\text{ and }x\neq 1$$

Steps for Solving Linear Equation

Multiply both sides of the equation by \left(x-1\right)\left(x+2\right), the least common multiple of \left(x+2\right)\left(x-1\right),x+2,x-1.

$$3x+2=\left(x-1\right)m+\left(x+2\right)n$$

Use the distributive property to multiply x-1 by m.

$$3x+2=xm-m+\left(x+2\right)n$$

Use the distributive property to multiply x+2 by n.

$$3x+2=xm-m+xn+2n$$

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

$$xm-m+xn+2n=3x+2$$

Subtract xm from both sides.

$$-m+xn+2n=3x+2-xm$$

Add m to both sides.

$$xn+2n=3x+2-xm+m$$

Combine all terms containing n.

$$\left(x+2\right)n=3x+2-xm+m$$

The equation is in standard form.

$$\left(x+2\right)n=2+m+3x-mx$$

Divide both sides by x+2.

$$\frac{\left(x+2\right)n}{x+2}=\frac{2+m+3x-mx}{x+2}$$

Dividing by x+2 undoes the multiplication by x+2.

$$n=\frac{2+m+3x-mx}{x+2}$$