Solve tf(x)=x^2-2x+1/(x-1)

$$t f ( x ) = \frac { x ^ { 2 } - 2 x + 1 } { ( x - 1 ) }$$

Solve for f

$$f=\frac{x-1}{tx}$$

$$x\neq 0\text{ and }t\neq 0\text{ and }x\neq 1$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x-1.

$$tfx\left(x-1\right)=x^{2}-2x+1$$

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

$$tfx^{2}-tfx=x^{2}-2x+1$$

Combine all terms containing f.

$$\left(tx^{2}-tx\right)f=x^{2}-2x+1$$

Divide both sides by tx^{2}-tx.

$$\frac{\left(tx^{2}-tx\right)f}{tx^{2}-tx}=\frac{\left(x-1\right)^{2}}{tx^{2}-tx}$$

Dividing by tx^{2}-tx undoes the multiplication by tx^{2}-tx.

$$f=\frac{\left(x-1\right)^{2}}{tx^{2}-tx}$$

Divide \left(x-1\right)^{2} by tx^{2}-tx.

$$f=\frac{x-1}{tx}$$

Solve for t

$$t=\frac{x-1}{fx}$$

$$x\neq 0\text{ and }f\neq 0\text{ and }x\neq 1$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x-1.

$$tfx\left(x-1\right)=x^{2}-2x+1$$

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

$$tfx^{2}-tfx=x^{2}-2x+1$$

Combine all terms containing t.

$$\left(fx^{2}-fx\right)t=x^{2}-2x+1$$

Divide both sides by fx^{2}-fx.

$$\frac{\left(fx^{2}-fx\right)t}{fx^{2}-fx}=\frac{\left(x-1\right)^{2}}{fx^{2}-fx}$$

Dividing by fx^{2}-fx undoes the multiplication by fx^{2}-fx.

$$t=\frac{\left(x-1\right)^{2}}{fx^{2}-fx}$$

Divide \left(x-1\right)^{2} by fx^{2}-fx.

$$t=\frac{x-1}{fx}$$