Question 647873
Here are your original equations: {{{(8/(r-12))}}} = {{{(12/(r+10))}}}

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, {{{(r-12)(r+10)}}} 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.

{{{((r-12)(r+10))/(1)}}}{{{(8/(r-12))}}}={{{((r-12)(r+10))/(1)}}}{{{(12/(r+10))}}}

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 {{{(r-12)}}} denominator with the {{{(r-12)}}} numerator, leaving you with just {{{8(r+10)}}} on the top of the fraction.

You are left with {{{8(r+10)}}} on the top because you are multiplying {{{8}}} to {{{(r+10)}}}

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 {{{(r+10)}}} denominator with the {{{(r+10)}}} numerator, leaving you with just {{{12(r-12)}}} on the top of the fraction.

You are left with {{{12(r-12)}}} on the top because you are multiplying {{{12}}} to {{{(r-12)}}}

Here's what the equation looks like now:

{{{8(r+10)}}} = {{{12(r-12)}}}

Step 4: Distribute to the parenthesis

{{{8r+80}}} = {{{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+80}}} = {{{12r-144}}}
{{{8r+224}}} = {{{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}}}