trying to reduce to simpilest form
1.t-a/t^2-a^2 i have 1/2(t+a)
2.3y^3+7y^2+4y/y^2+5y+4 i have cannot reduce thanks
first one you should have had
(t-a)/((t+a)(t-a))
= 1/(t+a), I don't know where you got the 1/2 from
for the second one, it factors
y(3y+4)(y+1)/((y+1)(y+4))
let me know what you got
thanks i got could't reduce on the second one the first one the denominator both numbers are to the second power does that matter
To reduce the expressions to their simplest form, we need to factorize the numerators and denominators and then cancel out any common factors.
1. Simplifying (t-a)/(t^2-a^2):
The numerator and denominator in this expression are both binomials, and we can recognize that they represent a difference of squares. We can write t^2 - a^2 as (t+a)(t-a).
Therefore, the expression becomes:
(t-a)/(t^2-a^2) = (t-a)/[(t+a)(t-a)]
Now, we can cancel out the common factor of (t-a) from the numerator and denominator:
(t-a)/(t^2-a^2) = 1/(t+a)
So, the simplified form of (t-a)/(t^2-a^2) is 1/(t+a).
2. Simplifying (3y^3+7y^2+4y)/(y^2+5y+4):
In this expression, we can factorize both the numerator and denominator.
The numerator is a trinomial that can be factored as:
3y^3 + 7y^2 + 4y = y(3y^2 + 7y + 4)
The denominator is also a trinomial that can be factored as:
y^2 + 5y + 4 = (y+1)(y+4)
Now, we can rewrite the expression with the factored forms:
(3y^3+7y^2+4y)/(y^2+5y+4) = [y(3y^2 + 7y + 4)]/[(y+1)(y+4)]
Since there are no common factors between the numerator and denominator, this expression cannot be further simplified. So, the simplest form of (3y^3+7y^2+4y)/(y^2+5y+4) is [y(3y^2 + 7y + 4)]/[(y+1)(y+4)].