Solve y-1=2/x+3

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

Solve for x

$$x=-\frac{5-3y}{1-y}$$

$$y\neq 1$$

Steps for Solving Linear Equation

Variable x cannot be equal to -3 since division by zero is not defined. Multiply both sides of the equation by x+3.

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

Use the distributive property to multiply x+3 by y.

$$xy+3y+\left(x+3\right)\left(-1\right)=2$$

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

$$xy+3y-x-3=2$$

Subtract 3y from both sides.

$$xy-x-3=2-3y$$

Add 3 to both sides.

$$xy-x=2-3y+3$$

Add 2 and 3 to get 5.

$$xy-x=5-3y$$

Combine all terms containing x.

$$\left(y-1\right)x=5-3y$$

Divide both sides by y-1.

$$\frac{\left(y-1\right)x}{y-1}=\frac{5-3y}{y-1}$$

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

$$x=\frac{5-3y}{y-1}$$

Variable x cannot be equal to -3.

$$x=\frac{5-3y}{y-1}\text{, }x\neq -3$$

Solve for y

$$y=\frac{x+5}{x+3}$$

$$x\neq -3$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x+3.

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

Use the distributive property to multiply x+3 by y.

$$xy+3y+\left(x+3\right)\left(-1\right)=2$$

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

$$xy+3y-x-3=2$$

Add x to both sides.

$$xy+3y-3=2+x$$

Add 3 to both sides.

$$xy+3y=2+x+3$$

Add 2 and 3 to get 5.

$$xy+3y=5+x$$

Combine all terms containing y.

$$\left(x+3\right)y=5+x$$

The equation is in standard form.

$$\left(x+3\right)y=x+5$$

Divide both sides by x+3.

$$\frac{\left(x+3\right)y}{x+3}=\frac{x+5}{x+3}$$

Dividing by x+3 undoes the multiplication by x+3.

$$y=\frac{x+5}{x+3}$$