Question

Write each rational expression in simplest form. State all restrictions on the variables.
𝑥^2−10𝑥/5x

Answer 1

To simplify the rational expression (𝑥^2−10𝑥)/(5𝑥), we first factor the numerator and see if there are any common factors between the numerator and the denominator that can be canceled out.

The numerator 𝑥^2−10𝑥 can be factored as 𝑥(𝑥−10). Therefore, the rational expression becomes:

(𝑥^2−10𝑥)/(5𝑥) = (𝑥(𝑥−10))/(5𝑥)

Now, we can cancel out the common factor of 𝑥 between the numerator and the denominator:

(𝑥(𝑥−10))/(5𝑥) = (𝑥(𝑥−10))/(5) = (𝑥−10)/5

So, the simplified form of the rational expression is (𝑥−10)/5.

Now, let's state the restrictions on the variable 𝑥. Since the variable 𝑥 is in the denominator of the original rational expression (5𝑥), the value of 𝑥 cannot be zero. Therefore, the restriction on the variable 𝑥 is that 𝑥 cannot be equal to zero.