I am having a problem solving these problems could you please help me! Simplify by removing the factor of 1, y^2-25/5-y, 4y-12/4y
In the first, change it to
-(y^2-25)/(y-5) then factor the numberator as a difference of two squares (y+5)(y-5)
On the second, notice you can factor 4 out of the numerator, and the denominator, (then the 4/4 becomes 1)
Of course! I'd be happy to help you simplify these expressions.
Let's start with the first expression: (y^2-25)/(5-y).
To simplify this expression, we'll first look for common factors to cancel out. In this case, we can factor the numerator as the difference of squares: (y^2-25) = (y+5)(y-5).
Next, we can observe that there is a negative sign in the denominator, so we can factor it out: (5-y) = -(y-5).
Now, our expression becomes: [(y+5)(y-5)]/[-(y-5)].
We can cancel out the common factor of (y-5) from the numerator and denominator, which simplifies the expression further:
(y+5)/-1.
Finally, we can remove the factor of 1 to obtain the simplified expression of -(y+5), or -y-5.
Now, let's move on to the second expression: (4y-12)/(4y).
To simplify this expression, we'll first look for common factors to cancel out. In this case, we can observe that both the numerator and denominator have a common factor of 4.
Dividing each term by 4, we get: (y - 3)/y.
And there you have it! The simplified expression is (y - 3)/y.
Remember, when simplifying expressions, it's important to factor, cancel out common factors, and simplify terms as much as possible.