Show each step in simplifying the following rational expressions.
Also explain what a simplified rational expression looks like
(how you know it is simplified).
-15x^3·y^3/-20x·y^4
-15x3y3
———————
20xy4
Since 5 divides evenly into both -15 and 20, we divide each of these
coefficients by 5:
-3
-15x3y3
———————
20xy4
4
-3x3y3
———————
4xy4
Give the x in the bottom the exponent of 1
-3x3y3
———————
4x1y4
Now the rule is:
When dividing exponentials with like bases, subtract the exponents
(larger minus smaller) and put the result in place of the exponential
which had the larger exponent, and eliminate the exponential with the
smaller exponent.
Using the above rule:
x3 and x1 have like bases so we subtract exponents, larger minus smaller,
3 - 1, getting 2, and place x2 in place of x3, then eliminate the x1
-3x2y3
———————
4y4
Using the above rule again:
y3 and y4 have like bases so we subtract exponents, larger minus smaller,
4 - 3, getting 1, and place y1 in place of y4, then eliminate the y3:
-3x2
———————
4y1
Now we eliminate the 1 exponent of y1
-3x2
———————
4y
If we like we can also move the negative sign from the numerator out
in front of the whole fraction.
3x2
— ——————
4y
We know this is simplified because there are no common factors of the
numerator and denominator (other than 1), and also because there are no
exponentials with like bases.
Edwin
AnlytcPhil@aol.com