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 simplify the numerator and the denominator separately.
For the numerator, 15x^2y^4z, we can simplify it by dividing each term by the greatest common factor (GCF), which is 15xy^4z.
15x^2y^4z / 15xy^4z = (15/15) * (x^2/x) * (y^4/y^4) * (z/z) = (1)(x)(1)(1) = x.
Now, for the denominator, 3xy^5, we divide each term by the GCF, which is 3xy^5.
3xy^5 / 3xy^5 = (3/3) * (x/x) * (y^5/y^5) = (1)(1)(1) = 1.
Therefore, the simplified rational expression is just x/1, which is equivalent to x. The restriction on the variables is that y cannot equal 0 since it appears in the denominator term y^5.