Graph (y^2-2y+1)/(2y-3)

Math
y2-2y+12y-3
Find where the expression (y-1)22y-3 is undefined.
y=32
x=(y-1)22y-3 is an equation of a line, which means there are no horizontal asymptotes.
No Horizontal Asymptotes
Find the oblique asymptote using polynomial division.
Tap for more steps…
Factor using the perfect square rule.
Tap for more steps…
Rewrite 1 as 12.
y2-2y+122y-3
Check the middle term by multiplying 2ab and compare this result with the middle term in the original expression.
2ab=2⋅y⋅-1
Simplify.
2ab=-2y
Factor using the perfect square trinomial rule a2-2ab+b2=(a-b)2, where a=y and b=-1.
(y-1)22y-3
(y-1)22y-3
Expand (y-1)2.
Tap for more steps…
Rewrite (y-1)2 as (y-1)(y-1).
(y-1)(y-1)2y-3
Apply the distributive property.
y(y-1)-1(y-1)2y-3
Apply the distributive property.
y⋅y+y⋅-1-1(y-1)2y-3
Apply the distributive property.
y⋅y+y⋅-1-1y-1⋅-12y-3
Reorder y and -1.
y⋅y-1y-1y-1⋅-12y-3
Raise y to the power of 1.
y⋅y-1y-1y-1⋅-12y-3
Raise y to the power of 1.
y⋅y-1y-1y-1⋅-12y-3
Use the power rule aman=am+n to combine exponents.
y1+1-1y-1y-1⋅-12y-3
Add 1 and 1.
y2-1y-1y-1⋅-12y-3
Multiply -1 by -1.
y2-1y-1y+12y-3
Subtract 1y from -1y.
y2-2y+12y-3
y2-2y+12y-3
Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of 0.
2y3y22y+1
Divide the highest order term in the dividend y2 by the highest order term in divisor 2y.
y2
2y3y22y+1
Multiply the new quotient term by the divisor.
y2
2y3y22y+1
+y23y2
The expression needs to be subtracted from the dividend, so change all the signs in y2-3y2
y2
2y3y22y+1
y2+3y2
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
y2
2y3y22y+1
y2+3y2
y2
Pull the next terms from the original dividend down into the current dividend.
y2
2y3y22y+1
y2+3y2
y2+1
Divide the highest order term in the dividend -y2 by the highest order term in divisor 2y.
y214
2y3y22y+1
y2+3y2
y2+1
Multiply the new quotient term by the divisor.
y214
2y3y22y+1
y2+3y2
y2+1
y2+34
The expression needs to be subtracted from the dividend, so change all the signs in -y2+34
y214
2y3y22y+1
y2+3y2
y2+1
+y234
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
y214
2y3y22y+1
y2+3y2
y2+1
+y234
+14
The final answer is the quotient plus the remainder over the divisor.
y2-14+14(2y-3)
The oblique asymptote is the polynomial portion of the long division result.
y=y2-14
y=y2-14
This is the set of all asymptotes.
Vertical Asymptotes: y=32
No Horizontal Asymptotes
Oblique Asymptotes: y=y2-14
Graph (y^2-2y+1)/(2y-3)

Download our
App from the store

Create a High Performed UI/UX Design from a Silicon Valley.

Scroll to top