Home > Algebra > Excluded Values for Rational Expressions

How do you simplify #(y^2+10y+16)/(y+2)# and find the excluded values?

Answer 1

Factor the trinomial divide out the binomial in the denominator
#y = -2# is excluded because it would result in an undefined value.

#( y^2 + 10y + 16 )/(y+2)= { ( y +2) xx (y+8)}/(y + 2)#

Divide out the common factor of #( y + 2 )# this leaves.

#( y + 8 ) #

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Kennedy Adams

To simplify (y^2+10y+16)/(y+2), we can use the method of long division or synthetic division.

Using long division, we divide y^2+10y+16 by y+2. The result is y+8 with a remainder of 0.

Therefore, (y^2+10y+16)/(y+2) simplifies to y+8.

To find the excluded values, we set the denominator, y+2, equal to zero and solve for y.

y+2 = 0 y = -2

Hence, the excluded value is y = -2.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.