Simplify. State the nonpermissible values.
4a^2-1/4a^2-16*2-a/2a-1
This is what I did to try and solve it out:
(2a+1)(2a-1)/(2a+4)(2a-4)*2-a/(2a-1)
I cancelled out the (2a-1)'s and don't get how to solve.
I'm supposed to get the answer :
-2a-1/4(a+2)
But I don't get how to get that^.
an (2a-4)=2(a-2) or -2(2-a) which will cancel out your 2-a,
then do the same for the 2a+4, and this should give you your answer
Thanks so much =)
I read that as
(4a^2-1)/(4a^2-16) * (2-a)/(2a-1) , my brackets are necessary
= (2a+1)(2a-1)/( 4(a+2)(a-2) * (2-a)/(2a-1)
the (2-a)/(a-2) are opposite, they will give you the -1
so..
= -(2a+1)/(4(a+2)) , again you have to use brackets to write it on here.
Thanks Reiny =) But I to get everything clear, the 2-a and the a-2 cancel right? After I cancel those I am left with (2a+1) as the numerator:S Sorry I am just confused. Also did you factor out the 2a+4 and 2a-4 to get 4(a+2)(a-2)? Could you please explain step by step?
To simplify the expression and find the nonpermissible values, follow these steps:
Step 1: Identify and factor the numerator.
The numerator is 4a^2 - 1. This is a difference of squares, so it can be factored as (2a)^2 - 1^2 = (2a + 1)(2a - 1).
Step 2: Identify and factor the denominator.
The denominator is 4a^2 - 16. This is a difference of squares, so it can be factored as (2a)^2 - 4^2 = (2a + 4)(2a - 4).
Step 3: Simplify the expression.
Now that we have factored numerator and denominator, the expression becomes:
[(2a + 1)(2a - 1)] / [(2a + 4)(2a - 4)] * (2 - a) / (2a - 1)
Step 4: Cancel out common factors.
We can cancel out the common factors of (2a - 1) from the numerator and the denominator.
[(2a + 1) * 1] / [(2a + 4)(2a - 4)] * (2 - a) / 1
Simplifying further:
(2a + 1) / [(2a + 4)(2a - 4)] * (2 - a)
Step 5: Simplify further and find the nonpermissible values.
To simplify the expression, we can break up (2 - a) as (-1)(a - 2):
(2a + 1) / [(2a + 4)(2a - 4)] * (-1) * (a - 2)
Now we can multiply the numerators and denominators:
-(2a + 1)(a - 2) / [(2a + 4)(2a - 4)]
Expanding the numerator:
-(2a^2 - 3a - 2) / [(2a + 4)(2a - 4)]
At this point, we have simplified the expression. The nonpermissible values are the values of 'a' that make the denominator zero (since division by zero is undefined). To find these values, set the denominator equal to zero and solve:
(2a + 4)(2a - 4) = 0
2a + 4 = 0 or 2a - 4 = 0
2a = -4 or 2a = 4
a = -2 or a = 2
So, the nonpermissible values for 'a' are -2 and 2.
Finally, the simplified expression is -(2a^2 - 3a - 2) / [(2a + 4)(2a - 4)], which matches the expected answer of -2a - 1 / 4(a + 2).