SOLUTION: I need help with the following Algebra equation. Thank you very much. 8/r-12 = 12/r+10 (They are fractions, 8 over r-12) Thanks!

Algebra ->  Equations -> SOLUTION: I need help with the following Algebra equation. Thank you very much. 8/r-12 = 12/r+10 (They are fractions, 8 over r-12) Thanks!      Log On


   

Question 647873: I need help with the following Algebra equation. Thank you very much.
8/r-12 = 12/r+10
(They are fractions, 8 over r-12) Thanks!
Found 2 solutions by Algebraic, MathTherapy:
Answer by Algebraic(50) About Me  (Show Source):
You can put this solution on YOUR website!
Here are your original equations: %288%2F%28r-12%29%29 = %2812%2F%28r%2B10%29%29
These types of equations can be solved when you have the same LCD under both equations.
To find the LCD (least common denominator) of both of these equations, multiply both denominators together and that's the LCD.
So, %28r-12%29%28r%2B10%29 is the LCD.
Multiply the LCD to the numerator of each equation so that you can get rid of the denominator. Our goal is to get rid of the denominators.
Step 1: Get rid of the denominators by multiplying the numerator of each fraction by the LCD.
%28%28r-12%29%28r%2B10%29%29%2F%281%29%288%2F%28r-12%29%29=%28%28r-12%29%28r%2B10%29%29%2F%281%29%2812%2F%28r%2B10%29%29
Step 2: Cancel out what you can from the numerator and denominator of the left side fraction
You see that on the left side of the equation, you can cancel out the %28r-12%29 denominator with the %28r-12%29 numerator, leaving you with just 8%28r%2B10%29 on the top of the fraction.
You are left with 8%28r%2B10%29 on the top because you are multiplying 8 to %28r%2B10%29
Step 3: Cancel out what you can from the numerator and denominator of the right side fraction
You see that on the right side of the equation, you can cancel out the %28r%2B10%29 denominator with the %28r%2B10%29 numerator, leaving you with just 12%28r-12%29 on the top of the fraction.
You are left with 12%28r-12%29 on the top because you are multiplying 12 to %28r-12%29
Here's what the equation looks like now:
8%28r%2B10%29 = 12%28r-12%29
Step 4: Distribute to the parenthesis
8r%2B80 = 12r-144
Step 5: Combine like terms.. we are going to add '144' to both sides so we don't have to deal with negatives
8r%2B80 = 12r-144
8r%2B224 = 12r
Step 6: Combine like terms.. we are going to subtract '8r' to both sides so we don't have to deal with negatives
224 = 4r
Step 7: Divide '224' by '4' to get the 'r' by itself
224 = 4r
56 = r
Your answer is r = 56

Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!

I need help with the following Algebra equation. Thank you very much.
8/r-12 = 12/r+10
(They are fractions, 8 over r-12) Thanks!

8%2F%28r+-+12%29+=+12%2F%28r+%2B+10%29

12(r - 12) = 8(r + 10) ------ Cross-multiplying

12r - 144 = 8r + 80

12r - 8r = 80 + 144

4r = 224

r = 224%2F4, or highlight_green%2856%29

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