Answer:
The given fraction [tex]\frac{x^3-x^2}{x^3}[/tex] reduces to [tex]\frac{x-1}{x}[/tex]
Step-by-step explanation:
Consider the given fraction [tex]\frac{x^3-x^2}{x^3}[/tex]
We have to reduce the fraction to the lowest terms.
Consider numerator [tex]x^3-x^2[/tex]
We can take x² common from both the term,
Thus, numerator can be written as [tex]x^2(x-1)[/tex]
Given expression can be rewritten as ,
[tex]\frac{x^3-x^2}{x^3}=\frac{x^2(x-1)}{x^3}[/tex]
We can now cancel [tex]x^2[/tex] from both numerator and denominator,
[tex]\Rightarrow \frac{x^2(x-1)}{x^3}=\frac{x^2(x-1)}{x^2 \cdot x}[/tex]
[tex]\Rightarrow \frac{(x-1)}{x^2 \cdot x}=\frac{x-1}{x}[/tex]
Thus, the given fraction [tex]\frac{x^3-x^2}{x^3}[/tex] reduces to [tex]\frac{x-1}{x}[/tex]
