Solve (1-k)x^2+x+(1-k)=0t

$$( 1 - k ) x ^ { 2 } + x + ( 1 - k ) = 0 t$$

Solve for k

$$k=\frac{x^{2}+x+1}{x^{2}+1}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 1-k by x^{2}.

$$x^{2}-kx^{2}+x+1-k=0t$$

Anything times zero gives zero.

$$x^{2}-kx^{2}+x+1-k=0$$

Subtract x^{2} from both sides. Anything subtracted from zero gives its negation.

$$-kx^{2}+x+1-k=-x^{2}$$

Subtract x from both sides.

$$-kx^{2}+1-k=-x^{2}-x$$

Subtract 1 from both sides.

$$-kx^{2}-k=-x^{2}-x-1$$

Combine all terms containing k.

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

Divide both sides by -x^{2}-1.

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

Dividing by -x^{2}-1 undoes the multiplication by -x^{2}-1.

$$k=\frac{-x^{2}-x-1}{-x^{2}-1}$$

Divide -x^{2}-x-1 by -x^{2}-1.

$$k=\frac{x^{2}+x+1}{x^{2}+1}$$

Solve for t

$$t\in \mathrm{R}$$

$$k=\frac{x^{2}+x+1}{x^{2}+1}$$