Struggling to rearrange equation

  • Thread starter spiruel
  • Start date
  • #1
8
0
I'm trying to prove that

$$\dfrac{l}{c+u}+\dfrac{l}{c-u}=\dfrac{2l}{\sqrt{c^2-u^2}}$$


My workings so far:
$$\dfrac{l}{c+u}+\dfrac{l}{c-u},$$
put over common denominator,
$$\dfrac{l(c-u)}{(c-u)(c+u)}+\dfrac{l(c+u)}{(c-u)(c+u)},$$
$$\dfrac{l(c-u)+l(c+u)}{(c-u)(c+u)},$$
expand out,
$$\dfrac{cl-lu+cl+lu}{(c-u)(c+u)},$$
group up and cancel out,
$$\dfrac{2cl}{c^2-u^2},$$

we need to make it equal to
$$\dfrac{2l}{\sqrt{c^2-u^2}}$$
HOW?!?
 
Last edited:

Answers and Replies

  • #2
vela
Staff Emeritus
Science Advisor
Homework Helper
Education Advisor
14,846
1,416
I'm trying to prove that

$$\dfrac{l}{c+u}+\dfrac{l}{c-u}=\dfrac{2l}{\sqrt{c^2-u^2}}$$


My workings so far:
$$\dfrac{l}{c+u}+\dfrac{l}{c-u},$$
put over common denominator,
$$\dfrac{l(c-u)}{(c-u)(c+u)}+\dfrac{l(c+u)}{(c-u)(c+u)},$$
$$\dfrac{l(c-u)+l(c+u)}{(c-u)(c+u)},$$
expand out,
$$\dfrac{cl-lu+cl+lu}{(c-u)(c+u)},$$
group up and cancel out,
$$\dfrac{2cl}{c^2-u^2},$$

we need to make it equal to
$$\dfrac{2l}{\sqrt{c^2-u^2}}$$
HOW?!?
You can't because they're not equal. It's more apparent when you rewrite each slightly:
$$\frac{2cl}{c^2-u^2} = \frac{2cl}{c^2[1-(u/c)^2]} = \frac{2l}{c}\frac{1}{1-(u/c)^2}$$ and
$$\frac{2l}{\sqrt{c^2-u^2}} = \frac{2l}{\sqrt{c^2[1-(u/c)^2]}} = \frac{2l}{c}\frac{1}{\sqrt{1-(u/c)^2}}$$
 
  • #3
PeroK
Science Advisor
Homework Helper
Insights Author
Gold Member
2020 Award
15,664
7,789
There's no law against plugging some numbers in! If you're not sure whether two expressions are equal, try some numbers and see! l = 1, u = 1 and c = 2 proves a lack of equality here.
 

Related Threads on Struggling to rearrange equation

  • Last Post
2
Replies
28
Views
1K
  • Last Post
Replies
10
Views
3K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
3
Views
3K
  • Last Post
Replies
1
Views
1K
  • Last Post
2
Replies
28
Views
43K
  • Last Post
Replies
4
Views
1K
Top