Solve 6x^3/15x^4-60x^3=2/5(x-4)

$$\frac { 6 x ^ { 3 } } { 15 x ^ { 4 } - 60 x ^ { 3 } } = \frac { 2 } { 5 ( x - 4 ) }$$

Solve for x (complex solution)

$$x\in \mathrm{C}\setminus 0,4$$

Solution Steps

Variable x cannot be equal to any of the values 0,4 since division by zero is not defined. Multiply both sides of the equation by 15\left(x-4\right)x^{3}, the least common multiple of 15x^{4}-60x^{3},5\left(x-4\right).

$$6x^{3}=3x^{3}\times 2$$

Multiply 3 and 2 to get 6.

$$6x^{3}=6x^{3}$$

Subtract 6x^{3} from both sides.

$$6x^{3}-6x^{3}=0$$

Combine 6x^{3} and -6x^{3} to get 0.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any x.

$$x\in \mathrm{C}$$

Variable x cannot be equal to any of the values 0,4.

$$x\in \mathrm{C}\setminus 0,4$$

Solve for x

$$x\in \mathrm{R}\setminus 4,0$$

Solution Steps

Variable x cannot be equal to any of the values 0,4 since division by zero is not defined. Multiply both sides of the equation by 15\left(x-4\right)x^{3}, the least common multiple of 15x^{4}-60x^{3},5\left(x-4\right).

$$6x^{3}=3x^{3}\times 2$$

Multiply 3 and 2 to get 6.

$$6x^{3}=6x^{3}$$

Subtract 6x^{3} from both sides.

$$6x^{3}-6x^{3}=0$$

Combine 6x^{3} and -6x^{3} to get 0.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any x.

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

Variable x cannot be equal to any of the values 0,4.

$$x\in \mathrm{R}\setminus 0,4$$