Solve 3x-2/x+1=2+m/m+1

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

Solve for m

$$m=\frac{x-4}{5}$$

$$x\neq -1$$

Steps for Solving Linear Equation

Variable m cannot be equal to -1 since division by zero is not defined. Multiply both sides of the equation by \left(m+1\right)\left(x+1\right), the least common multiple of x+1,m+1.

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

Use the distributive property to multiply m+1 by 3x-2.

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

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

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

Use the distributive property to multiply mx+m+x+1 by 2.

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

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

$$3mx-2m+3x-2=2mx+2m+2x+2+xm+m$$

Combine 2mx and xm to get 3mx.

$$3mx-2m+3x-2=3mx+2m+2x+2+m$$

Combine 2m and m to get 3m.

$$3mx-2m+3x-2=3mx+3m+2x+2$$

Subtract 3mx from both sides.

$$3mx-2m+3x-2-3mx=3m+2x+2$$

Combine 3mx and -3mx to get 0.

$$-2m+3x-2=3m+2x+2$$

Subtract 3m from both sides.

$$-2m+3x-2-3m=2x+2$$

Combine -2m and -3m to get -5m.

$$-5m+3x-2=2x+2$$

Subtract 3x from both sides.

$$-5m-2=2x+2-3x$$

Combine 2x and -3x to get -x.

$$-5m-2=-x+2$$

Add 2 to both sides.

$$-5m=-x+2+2$$

Add 2 and 2 to get 4.

$$-5m=-x+4$$

The equation is in standard form.

$$-5m=4-x$$

Divide both sides by -5.

$$\frac{-5m}{-5}=\frac{4-x}{-5}$$

Dividing by -5 undoes the multiplication by -5.

$$m=\frac{4-x}{-5}$$

Divide -x+4 by -5.

$$m=\frac{x-4}{5}$$

Variable m cannot be equal to -1.

$$m=\frac{x-4}{5}\text{, }m\neq -1$$

Solve for x

$$x=5m+4$$

$$m\neq -1$$

Solution Steps

Variable x cannot be equal to -1 since division by zero is not defined. Multiply both sides of the equation by \left(m+1\right)\left(x+1\right), the least common multiple of x+1,m+1.

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

Use the distributive property to multiply m+1 by 3x-2.

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

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

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

Use the distributive property to multiply mx+m+x+1 by 2.

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

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

$$3mx-2m+3x-2=2mx+2m+2x+2+xm+m$$

Combine 2mx and xm to get 3mx.

$$3mx-2m+3x-2=3mx+2m+2x+2+m$$

Combine 2m and m to get 3m.

$$3mx-2m+3x-2=3mx+3m+2x+2$$

Subtract 3mx from both sides.

$$3mx-2m+3x-2-3mx=3m+2x+2$$

Combine 3mx and -3mx to get 0.

$$-2m+3x-2=3m+2x+2$$

Subtract 2x from both sides.

$$-2m+3x-2-2x=3m+2$$

Combine 3x and -2x to get x.

$$-2m+x-2=3m+2$$

Add 2m to both sides.

$$x-2=3m+2+2m$$

Combine 3m and 2m to get 5m.

$$x-2=5m+2$$

Add 2 to both sides.

$$x=5m+2+2$$

Add 2 and 2 to get 4.

$$x=5m+4$$

Variable x cannot be equal to -1.

$$x=5m+4\text{, }x\neq -1$$