i have a hard time understanding the non permissable values could someone please explain. I have solved the following equations but need help determining the values. Also if you could check to see if i did them right it would be alot of help
1. a2+7a+12/a2+4a+4 x a2-a-6/a2-9
(Ans)a+4/a+2
2.4/y2+5y+6 - 5/y2-y-12
(ans) -(y-26)/(y+2)(y+3)(y-4)
any number following a letter is to the power of
Nonpermissiable values.
You only have to worry about the denominators. A denominator can never be equal to zero since division by zero is not defined.
If a denominator is x + 2 , we don't want it to equal zero. So, x cannot = -2 sind that will cause the denominator to equal zero.
that makes much more sense thank you i couldn't figure it out
so a restriction is someting that it cannot be divded or multiplied from right?
ok that helped thank you
Non-permissible values, also known as excluded values or restrictions, are values that cannot be used in a mathematical expression because they would result in an undefined or impossible situation. These values often occur when we have divisions by zero or when an expression is not defined for certain inputs.
To determine the non-permissible values in an equation, you need to identify the situations that would cause division by zero or the creation of undefined terms. Here's how you can find them for the given equations:
1. Equation: (a^2 + 7a + 12)/(a^2 + 4a + 4) * (a^2 - a - 6)/(a^2 - 9)
In the first fraction, the denominator is a perfect square trinomial, which means it can be factored into a square of a binomial: (a + 2)^2. Since division by zero is not allowed, the non-permissible value occurs when (a + 2) equals zero. Therefore, a = -2 is a non-permissible value.
In the second fraction, the denominator is a difference of squares: (a + 3)(a - 3). It results in a non-permissible value when either (a + 3) equals zero or (a - 3) equals zero. So, a = -3 and a = 3 are non-permissible values.
Thus, the non-permissible values for this equation are a = -2, a = -3, and a = 3.
2. Equation: 4/(y^2 + 5y + 6) - 5/(y^2 - y - 12)
In the first fraction, the denominator can be factored into (y + 2)(y + 3), while the second fraction's denominator can be factored into (y + 4)(y - 3). The non-permissible values occur when any of these denominators equal zero.
For the first fraction, the non-permissible values are y = -2 and y = -3.
For the second fraction, the non-permissible values are y = -4 and y = 3.
Hence, the non-permissible values for this equation are y = -2, y = -3, y = -4, and y = 3.
To validate your answers for the equations, you need to substitute the non-permissible values into the expressions and check if they lead to a division by zero or undefined terms. If any of the answers contain these non-permissible values, they would be considered incorrect.