Solve x-1/5{{left(frac{x/5right)}^3-1/5}}

$$\frac{ x-1 }{ \frac{ 5 }{ { \left( \frac{ x }{ 5 } \right) }^{ 3 } - \frac{ 1 }{ 5 } } }$$

Evaluate

$$\frac{\left(x-1\right)\left(x^{3}-25\right)}{625}$$

Solution Steps

Divide x-1 by \frac{5}{\left(\frac{x}{5}\right)^{3}-\frac{1}{5}} by multiplying x-1 by the reciprocal of \frac{5}{\left(\frac{x}{5}\right)^{3}-\frac{1}{5}}.

$$\frac{\left(x-1\right)\left(\left(\frac{x}{5}\right)^{3}-\frac{1}{5}\right)}{5}$$

To raise \frac{x}{5} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(x-1\right)\left(\frac{x^{3}}{5^{3}}-\frac{1}{5}\right)}{5}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5^{3} and 5 is 125. Multiply \frac{1}{5} times \frac{25}{25}.

$$\frac{\left(x-1\right)\left(\frac{x^{3}}{125}-\frac{25}{125}\right)}{5}$$

Since \frac{x^{3}}{125} and \frac{25}{125} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(x-1\right)\times \frac{x^{3}-25}{125}}{5}$$

Express \left(x-1\right)\times \frac{x^{3}-25}{125} as a single fraction.

$$\frac{\frac{\left(x-1\right)\left(x^{3}-25\right)}{125}}{5}$$

Express \frac{\frac{\left(x-1\right)\left(x^{3}-25\right)}{125}}{5} as a single fraction.

$$\frac{\left(x-1\right)\left(x^{3}-25\right)}{125\times 5}$$

Multiply 125 and 5 to get 625.

$$\frac{\left(x-1\right)\left(x^{3}-25\right)}{625}$$

Use the distributive property to multiply x-1 by x^{3}-25.

$$\frac{x^{4}-25x-x^{3}+25}{625}$$

Expand

$$\frac{x^{4}}{625}-\frac{x^{3}}{625}-\frac{x}{25}+\frac{1}{25}$$

Solution Steps

Divide x-1 by \frac{5}{\left(\frac{x}{5}\right)^{3}-\frac{1}{5}} by multiplying x-1 by the reciprocal of \frac{5}{\left(\frac{x}{5}\right)^{3}-\frac{1}{5}}.

$$\frac{\left(x-1\right)\left(\left(\frac{x}{5}\right)^{3}-\frac{1}{5}\right)}{5}$$

To raise \frac{x}{5} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(x-1\right)\left(\frac{x^{3}}{5^{3}}-\frac{1}{5}\right)}{5}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5^{3} and 5 is 125. Multiply \frac{1}{5} times \frac{25}{25}.

$$\frac{\left(x-1\right)\left(\frac{x^{3}}{125}-\frac{25}{125}\right)}{5}$$

Since \frac{x^{3}}{125} and \frac{25}{125} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(x-1\right)\times \frac{x^{3}-25}{125}}{5}$$

Express \left(x-1\right)\times \frac{x^{3}-25}{125} as a single fraction.

$$\frac{\frac{\left(x-1\right)\left(x^{3}-25\right)}{125}}{5}$$

Express \frac{\frac{\left(x-1\right)\left(x^{3}-25\right)}{125}}{5} as a single fraction.

$$\frac{\left(x-1\right)\left(x^{3}-25\right)}{125\times 5}$$

Multiply 125 and 5 to get 625.

$$\frac{\left(x-1\right)\left(x^{3}-25\right)}{625}$$

Use the distributive property to multiply x-1 by x^{3}-25.

$$\frac{x^{4}-25x-x^{3}+25}{625}$$