Question

how do you solve this equation just show me the steps to the answer, (12)/(y)+(12)/(y+1)=1,
the parentheses are just there to show you how the equation goes together.

Answer 1

Multiply both sides by y(y+1) and have a look at what you get ...

Answer 2

Show me I can't figure it out

Answer 3

Multiplying both sides by y(y+1)

12y(y+1)/y + 12y(y+1)/(y+1) = y(y+1)

So 12(y+1) + 12y = y^2 + y

Following?

Answer 4

Yes, Continue!

Answer 5

So

LHS = 12y + 12 + 12y = 24y + 12

Hence y^2 + y - (24y + 12) = 0
i.e., y^2 - 24y - 12 = 0

Yes? And now you can solve this quadratic equation

Answer 6

How did you get 24y+12?

Answer 7

The left hand side, the LHS = 12(y+ 1) + 12 = 12y + 12 + 12y = 24y + 12

Answer 8

ooooo I understand now thanks!

Answer 9

'good answer' if you don't mind

Answer 10

What grade are you in?

Answer 11

10th but I suck at math

Answer 12

got it. Write out this example with all the steps by yourself until you get it.

The start with a blank piece of paper and do it again. Repeat that until you can do it without looking. This way, you'll really learn this.

Please also give me a 'good answer'

Answer 13

Quick question first how did you get the 24y+12 out of the parentheses?

Answer 14

12(y+ 1) + 12y = 12y + 12 + 12y = 24y + 12

Answer 15

We had:
12(y+1) + 12y = y^2 + y

The LHS = 12(y+ 1) + 12y = 12y + 12 + 12y = 24y + 12

Answer 16

12/(y+1)+12/y = 1
Multiply both sides by y:
(12 y)/(y+1)+12 = y
Write the left hand side as a single fraction:
(12 (2 y+1))/(y+1) = y
Expand out terms of the left hand side:
(24 y)/(y+1)+12/(y+1) = y
Multiply both sides by y+1:
24 y+12 = y (y+1)
Expand out terms on the right hand side:
24 y+12 = y^2+y
Subtract (y^2+y) from both sides:
-y^2+23 y+12 = 0
Solve the quadratic equation by completing the square:

Divide both sides by -1:
y^2-23 y-12 = 0
Add 12 to both sides:
y^2-23 y = 12
Add 529/4 to both sides:
y^2-23 y+529/4 = 577/4
Factor the left hand side:
(y-23/2)^2 = 577/4
Take the square root of both sides:
sqrt(y-23/2) = sqrt(577)/2
Eliminate the absolute value:
y-23/2 = -sqrt(577)/2 or y-23/2 = sqrt(577)/2
Add 23/2 to both sides:
y = 1/2 (23-sqrt(577)) or y-23/2 = sqrt(577)/2
Add 23/2 to both sides:
y = 1/2 (23-sqrt(577)) or y = 1/2 (23+sqrt(577))

Answer 17

Thanks @JamesJ