# simplification

1. ### Need help with simplification of the DE

Hi all, I couldn't simplify exactly to get the correct answers(more then 1) for the attached multiple answers question. Attaching the steps done at my end as well. Thanks a lot in advance :)
2. ### rational expression simplification

Hi everyone, I couldn't do this: (x^2-y^2-4y-4) / (x^2-y^2-4y+4) any idea?
3. ### Negation & Simplification of Proposition

I am attempting to negate and simplify this proposition: $âˆƒ_x((p(x) âˆ§ q(x))$ My attempt to solve this: $$âˆ€_x(Â¬p(x) âˆ¨ Â¬ q(x))$$ $$âˆ€_x(p(x) âˆ§ q(x))$$ I'm not sure if I have correctly negated and simplified this proposition, so help would be greatly appreciated.
4. ### Simplification of a formula

We consider a fixed parameter $\theta>0$. For all $t>0$ we note: $$u(t)=\frac{\sinh\big(\frac{t}{2}\cosh(\theta)\big)}{\cosh(\theta)}$$ $$A(t)=\frac{\sqrt{\cosh^2(\theta)u^2(t)+1}-1}{\cosh^2(\theta)}-\Big(\cosh\Big(\frac{t}{2}\Big)-1\Big)$$...
5. ### Exponent simplification help needed

Below is a problem I did on khan academy, the first thing I did to simplify the problem was square the top and bottom, but in the solution they waited until the very end to take the square root which changed the answer. Was squaring the top and bottom first not the proper way to do it? I'm confused
6. ### simplification of the integral terms

Hi, I would like to know whether someone can explain the simplification which follows in the image, thanks!!

9. ### Set Theory and Simplification.

X and Y are two sets. Simplify the following: (Y âˆ’ X)âˆ©X Could somebody please help me with this question. I am really struggling with set theory. I understand that âˆ© means "and", and "-" is the relative complement (difference between sets).
10. ### Help with simplification

Can someone show me how the author arrived at the following results?
11. ### Advanced Boolean Algebraic Equations

Advanced Boolean Algebraic Equations Basic Equations(1&0) 1+1 = 1 1*1=1 1+0 = 1 1*0=0 0+0 = 0 0*0=0 A+1=1 A*1=A A+0=A A*0=0 A+A=A A*A=A A+A'=1 A*A'=0 Basic Equation(Variables) 1) A+AB = A 2) A+A'B = A+B 3) AB+AB' = A Advance Equation(Multi-variable) 1)...
12. ### Simplification help

if you have an integral with 1 -cos^2(x) in it and then apply the half angle formula and then get the integral of 1-(1/2*cos(4x)). How would you simplify it to get the integral of (1/2)-(1/2)*cos(4x). The problem is on the bottom of this page.. Calculus II - Integrals Involving Trig Functions
13. ### Help with simplification

This is from a slide on my course i was wondering about We have this: \frac{dp_{x}}{dt}=\frac{D}{D+S}+\frac{S}{D+B}* \left \{ \frac{S}{D+B}*\frac{dp_{x}}{dt} \right \} Apparently we can simplify it to this \frac{dp_{x}}{dt}=\frac{D}{(D+S)-\left [ \frac{S^2}{D+B} \right ]} How?
14. ### Integration Simplification

Can you please simplify and help me out for this Answer Integration of {(4x-1)* square root of(2x^2 -x + 1)} Question in verbally: integration of four ex minus 1 into square root of two ex square minus x plus 1..
15. ### Boolean Algebra simplification

Please see attachment for workings Hi guys I'm struggling to get this Boolean expression down to 3 expressions, I'm not sure if it is possible or if this is the final answer, iv'e tried a few different ways, but keep landing back at F=(B OR C OR NOT C OR NOT A) Any help or ideas to point me...
16. ### Logic Simplification

A fellow student has this posted in my uni forum from an old tute and when i tried it i got stumped to and cant figure it out. help please. The problem is we need to simplify the following pic, simplify so less IC's are used or save money or somthing I tried changing it to or gates then...
17. ### Boolean Algebra Simplification

Here is the problem A[BC + D]â€™E + ABDâ€™ Does [BC+D]' require DeMorgans Theorem or would distributing A be okay as first step? I tried both ways but I feel stuck I get to a point where it doesn't seem like it works.
18. ### Boolean algebra simplification using boolean rules

Hey guys, First off, sorry for the overly easy question. I need to prove this boolean expression using the Boolean logic rules. (Commutative, Associative, Distributive, Identity, Redundance, De Morgan...) (a or b) and (c or (not b)) = (a and (not b)) or (b and c) (a + b)(c + Â¬b) = a(Â¬b)...
19. ### Need help with simplification

How do I simplify the term in red box into the underlined term?
20. ### Simplification

Hello, Wolfram Alpha says: $\frac{4\tan 4x\sec 4x}{2\sqrt{\sec 4x}}=2\sin 4x{{\sec }^{\frac{3}{2}}}4x$ I obviously see that 4/2 = 2 but after that I'm just not sure. Can anyone help me out?