Solve a^237+a^238=a^237(a+1)

$$a ^ { 237 } + a ^ { 238 } = a ^ { 237 } ( a + 1 )$$

Solve for a (complex solution)

$$a\in \mathrm{C}$$

Solution Steps

Use the distributive property to multiply a^{237} by a+1.

$$a^{237}+a^{238}=a^{238}+a^{237}$$

Subtract a^{238} from both sides.

$$a^{237}+a^{238}-a^{238}=a^{237}$$

Combine a^{238} and -a^{238} to get 0.

$$a^{237}=a^{237}$$

Subtract a^{237} from both sides.

$$a^{237}-a^{237}=0$$

Combine a^{237} and -a^{237} to get 0.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any a.

$$a\in \mathrm{C}$$

Solve for a

$$a\in \mathrm{R}$$

Solution Steps

Use the distributive property to multiply a^{237} by a+1.

$$a^{237}+a^{238}=a^{238}+a^{237}$$

Subtract a^{238} from both sides.

$$a^{237}+a^{238}-a^{238}=a^{237}$$

Combine a^{238} and -a^{238} to get 0.

$$a^{237}=a^{237}$$

Subtract a^{237} from both sides.

$$a^{237}-a^{237}=0$$

Combine a^{237} and -a^{237} to get 0.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any a.

$$a\in \mathrm{R}$$