Solve y=2+(x-1)*1/x-5

$$y = 2 + ( x - 1 ) \times \frac { 1 } { x - 5 }$$

Solve for x

$$x=-\frac{5y-11}{3-y}$$

$$y\neq 3$$

Steps for Solving Linear Equation

Variable x cannot be equal to 5 since division by zero is not defined. Multiply both sides of the equation by x-5.

$$y\left(x-5\right)=\left(x-5\right)\times 2+\left(x-1\right)\times 1$$

Use the distributive property to multiply y by x-5.

$$yx-5y=\left(x-5\right)\times 2+\left(x-1\right)\times 1$$

Use the distributive property to multiply x-5 by 2.

$$yx-5y=2x-10+\left(x-1\right)\times 1$$

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

$$yx-5y=2x-10+x-1$$

Combine 2x and x to get 3x.

$$yx-5y=3x-10-1$$

Subtract 1 from -10 to get -11.

$$yx-5y=3x-11$$

Subtract 3x from both sides.

$$yx-5y-3x=-11$$

Add 5y to both sides.

$$yx-3x=-11+5y$$

Combine all terms containing x.

$$\left(y-3\right)x=-11+5y$$

The equation is in standard form.

$$\left(y-3\right)x=5y-11$$

Divide both sides by y-3.

$$\frac{\left(y-3\right)x}{y-3}=\frac{5y-11}{y-3}$$

Dividing by y-3 undoes the multiplication by y-3.

$$x=\frac{5y-11}{y-3}$$

Variable x cannot be equal to 5.

$$x=\frac{5y-11}{y-3}\text{, }x\neq 5$$

Solve for y

$$y=-\frac{11-3x}{x-5}$$

$$x\neq 5$$