SOLUTION: Ques-1 Simplify 1+(1/(1+x))+(1/(1+x))^2+.....infinite Ques-2 If. c+((d-y)/y)=e-1+(f/4)...then find the value of y. Ques-3 If. (4+3√3)/(√7+4√3)=A+&#87

Algebra ->  Equations -> SOLUTION: Ques-1 Simplify 1+(1/(1+x))+(1/(1+x))^2+.....infinite Ques-2 If. c+((d-y)/y)=e-1+(f/4)...then find the value of y. Ques-3 If. (4+3√3)/(√7+4√3)=A+&#87      Log On


   



Question 1093679: Ques-1
Simplify
1+(1/(1+x))+(1/(1+x))^2+.....infinite
Ques-2
If.
c+((d-y)/y)=e-1+(f/4)...then find the value of y.
Ques-3
If.
(4+3√3)/(√7+4√3)=A+√B....then find the value of B-A

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
Just two questions:

 

That's an infinite geometric series with first term a1=1 
and common ratio = r%22%22=%22%221%2F%281%2Bx%29.

The formula is S%5Binfinity%5D%22%22=%22%22a%5B1%5D%2F%281-r%29%22%22=%22%22matrix%281%2C3%2Ca%5B1%5D%2C%22%F7%22%2C%281-r%29%29

S%5Binfinity%5D%22%22=%22%22matrix%281%2C3%2C1%2C%22%F7%22%2C%281-1%2F%281%2Bx%29%29%29

S%5Binfinity%5D%22%22=%22%22matrix%281%2C3%2C1%2C%22%F7%22%2C%28%281%2Bx%29%2F%281%2Bx%29-1%2F%281%2Bx%29%29%29

S%5Binfinity%5D%22%22=%22%22matrix%281%2C3%2C1%2C%22%F7%22%2C%28%28%281%2Bx%29-1%29%2F%281%2Bx%29%29%29

S%5Binfinity%5D%22%22=%22%22matrix%281%2C3%2C1%2C%22%F7%22%2C%28%281%2Bx-1%29%2F%281%2Bx%29%29%29

S%5Binfinity%5D%22%22=%22%22matrix%281%2C3%2C1%2C%22%F7%22%2Cx%2F%281%2Bx%29%29

S%5Binfinity%5D%22%22=%22%22matrix%281%2C3%2C1%2C%22%22%2A%22%22%2C%281%2Bx%29%2Fx%29

S%5Binfinity%5D%22%22=%22%22%281%2Bx%29%2Fx
-----
c%2B%28%28d-y%29%2Fy%29%22%22=%22%22e-1%2B%28f%2F4%29

Multiply through by LCD = 4y

%284y%29c%2B%284y%29%28%28d-y%29%2Fy%29%22%22=%22%22%284y%29e-%284y%291%2B%284y%29%28f%2F4%29

4cy%2B%284cross%28y%29%29%28%28d-y%29%2Fcross%28y%29%29%22%22=%22%224ey-4y%2B%28cross%284%29y%29%28f%2Fcross%284%29%29

4cy%2B4%28d-y%29%22%22=%22%224ey-4y%2Bfy

4cy%2B4d-4y%22%22=%22%224ey-4y%2Bfy

Both side contain -4y so we add 4y to both sides
and they will cancel:

4cy%2B4d%22%22=%22%224ey%2Bfy

Get all three terms containing y on the left side,
and the term that does not contain y on the right:

4cy-4ey-fy%22%22=%22%22-4d

factor out y on the left side:

y%284c-4e-f%29%22%22=%22%22-4d

Divide both sides by (4c-4e-f)

y+%22%22=%22%22+%28-4d%29%2F%284c-4e-f%29

Edwin