# State any restrictions on the variable in the complex fraction. \frac{\frac{x-4}{x+4}}{\frac{x^{2}-1}{x}}

State any restrictions on the variable in the complex fraction. $$\displaystyle{\frac{{{\frac{{{x}-{4}}}{{{x}+{4}}}}}}{{{\frac{{{x}^{{{2}}}-{1}}}{{{x}}}}}}}$$

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Brighton

$$\displaystyle{\frac{{{x}-{4}}}{{{x}}}}={5}$$ By cross multiplication.
Multiply both sides by x
$$\displaystyle{\frac{{{x}-{4}}}{{{x}}}}\times{x}={5}\times{x}$$
5x=x-4 Multiplying the numbers
4x=-4 Subtracting x from both sides
$$\frac{4x}{4}=\frac{-4}{4}$$ Dividing both sides by 4
x=-1 Simplifying fractions