Write each rational expression in simplest form. State all restrictions on the variables
15x^2y^4z / 3xy^5
To simplify the rational expression 15x^2y^4z / 3xy^5, we can first simplify the coefficients and combine like terms:
15 / 3 = 5
Next, we can simplify the variables. For the x's, we subtract the exponents in the numerator and denominator: x^2 / x = x^(2-1) = x^1 = x. For the y's, we subtract the exponents in the numerator and denominator: y^4 / y^5 = y^(4-5) = y^(-1) = 1/y. Lastly, we have z in the numerator so it remains the same.
After simplifying the coefficients and variables, the rational expression becomes:
5xz / y
The restrictions on the variables come from any denominators that potentially could be equal to zero in order to prevent division by zero. In this case, the only restriction is that y cannot equal to zero.