Solve x^4+11/x^4+10=1+1/x^4+10

$$\frac { x ^ { 4 } + 11 } { x ^ { 4 } + 10 } = 1 + \frac { 1 } { x ^ { 4 } + 10 }$$

Solve for x

$$x\in \mathrm{R}$$

Solution Steps

Multiply both sides of the equation by x^{4}+10.

$$x^{4}+11=x^{4}+10+1$$

Add 10 and 1 to get 11.

$$x^{4}+11=x^{4}+11$$

Subtract x^{4} from both sides.

$$x^{4}+11-x^{4}=11$$

Combine x^{4} and -x^{4} to get 0.

$$11=11$$

Compare 11 and 11.

$$\text{true}$$

This is true for any x.

$$x\in \mathrm{R}$$

Solve for x (complex solution)

$$x\in \mathrm{C}\setminus \sqrt[4]{40}\left(\frac{1}{2}-\frac{1}{2}i\right),\sqrt[4]{40}\left(-\frac{1}{2}-\frac{1}{2}i\right),\sqrt[4]{40}\left(-\frac{1}{2}+\frac{1}{2}i\right),\sqrt[4]{40}\left(\frac{1}{2}+\frac{1}{2}i\right)$$