Solve 30.6/x-25/x/1+frac{30.6{x}25/x}=frac{5.6x}{x^2+765}

$$\frac{ \frac{ 30.6 }{ x } - \frac{ 25 }{ x } }{ 1+ \frac{ 30.6 }{ x } \frac{ 25 }{ x } } = \frac{ 5.6x }{ { x }^{ 2 } +765 }$$

Solve for x

$$x\neq 0$$

Solution Steps

Multiply both sides of the equation by x^{2}+765.

$$x^{2}\left(\frac{30.6}{x}-\frac{25}{x}\right)=5.6x$$

Use the distributive property to multiply x^{2} by \frac{30.6}{x}-\frac{25}{x}.

$$x^{2}\times \frac{30.6}{x}+x^{2}\left(-\frac{25}{x}\right)=5.6x$$

Express x^{2}\left(-\frac{25}{x}\right) as a single fraction.

$$x^{2}\times \frac{30.6}{x}+\frac{-x^{2}\times 25}{x}=5.6x$$

Multiply -1 and 25 to get -25.

$$x^{2}\times \frac{30.6}{x}+\frac{-25x^{2}}{x}=5.6x$$

Subtract 5.6x from both sides.

$$x^{2}\times \frac{30.6}{x}+\frac{-25x^{2}}{x}-5.6x=0$$

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$x^{2}\times 30.6-25x^{2}-5.6xx=0$$

Multiply x and x to get x^{2}.

$$x^{2}\times 30.6-25x^{2}-5.6x^{2}=0$$

Combine x^{2}\times 30.6 and -25x^{2} to get 5.6x^{2}.

$$5.6x^{2}-5.6x^{2}=0$$

Combine 5.6x^{2} and -5.6x^{2} 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 0.

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

Solve for x (complex solution)

$$x\in \mathrm{C}\setminus 0,-i\times 3\sqrt{85},i\times 3\sqrt{85}$$