Question

Evaluate the following: [(x+y)^2]/[4x^2-y^2] = ??? if x = 3 and y = -5d. I got the following: [(3+(-5d))^2]/[4(3)^2-(-5d)^2] => [9-30d+25d^2]/[36+25d^2]

Answer 1

Does it end up with: 9-30d/36?

Answer 2

Equation View: Evaluate the following if x = 3; y -5d
\[\frac{ (x+y)^{2} }{ 4x ^{2}-y ^{2} }\]

I got the following:
\[\frac{ (3+(-5d))^{2} }{ 4(9) ^{2}-(-5d) ^{2} }\]
\[\frac{ 9-30d+25d^{2} }{ 36+25d^{2} }\]

I cant figure out the next step.

Answer 3

Factoring it..

Answer 4

For the numerator rearrange it to
\(\ 25d^{2}-30d+9 \)

Answer 5

And we use the perfect square trinomial which is
\(\ A^2 - 2AB + B^2 = (A - B)^2\)

Answer 6

Do you get that? @Sadworld @~
:P

Answer 7

In this example we have \(\ \color{blue}{ A = 5x }\) and \(\ \color{red}{ B = 3 }\)

Answer 8

So
\(\ 25x^{2}-30x+9 = ( \color{blue}{ 5x } - \color{red}{ 3 } )^2\)

Answer 9

So you mean I should factor it? My answer would bet the same as the question: (3+(-5d))^2

Answer 10

I'm asked to simplify further. I'm wondering if 25d^2 cancel each other out making the it 9-30d/36

Answer 11

Looking at the denominator from the very beginning:

[4x^2-y^2]

= [36 - ( - 5d ) ^2 ]

= [ 36 - ( + 25 d^2) ]

= [ 36 - 25 d^2 }

Answer 12

I think you have the denominator as [ 36 + 25 d^2 }

Not sure, but please check. @Sadworld

Answer 13

I see, you're right

Answer 14

What I should do next after solving it? I'm asked to simplify further.

Answer 15

That denominator will not factor over the real numbers.

Answer 16

Let me look again at the numerator.

Answer 17

Just in case, would you double-check and see if you posted the problem correctly?

Answer 18

Could you paste the problem here?

Answer 19

Yeah, the problem is correct. I don't think it can be factored further. I just want to be sure.
Just a 2nd copy of the problem:

If x = 3 and y = -5b

\[\frac{ (x+y)^{2} }{ 4x ^{2}-y ^{2} }\]

Answer 20

Can you divided with 1/common deno?

Answer 21

basically cross multiply?

Answer 22

y = -5b ? or y = -5d ? as stated in the original post?

Answer 23

It's y = -5d; typo, sorry

Answer 24

I don't think the expression will simplify. Were you told that it would?

Answer 25

Nope, got it in a problem book. Just says to simply as much as possible. Cross multiply with itself isn't a possibility?

Answer 26

Cross multiply when there is an equation. There is no equation here.

Answer 27

I am going to rework the problem from the beginning and see if I get the same answer.
I will report back here on my result, okay?

Answer 28

Sure thing, I'll be online for awhile. I can check up tom is it takes longer.

Answer 29

It should go fast.

Answer 30

BTW, I've factored/simplified the originals question, dunno if it matters:
\[\frac{ (x+y)(x+y) }{ (2x+y)(2x-y) }\]

Answer 31

No common factors upstairs and downstairs.

Okay, my re-check gives

Numerator: (3 - 5d)^2

Denominator: (36 - 25 d^2) = ( 6 + 5d) (6 - 5d)

Answer 32

same here

Answer 33

I think that is the answer. Usually, these books read "simplify if possible" so as not to make us think the result should simplify.

Answer 34

Okay, thanks. So I've been knocking on my head for no reason. Well better try then be sorry :)

Answer 35

The "cleanest" way to write this,I think, is with

Numerator: (3 - 5d)^2

Denominator: (36 - 25 d^2)

Answer 36

Right, I agree. And, we did find a sign error even if it did not allow us to strike out factors.

Answer 37

Hey, if this turns out to be a different answer, would you post here and let me know.

I just cannot imagine what a different answer would be.

Answer 38

Sure thing, if there's no answer then we got it right :D

Answer 39

I'm laughing at that. And, I enjoyed exchanging math ideas with you. Let's do it again sometime, okay?