Hi, there--

THE PROBLEM:
Solve for w.
(w-3)/(w+2)=(6-w)/(w-12)

A SOLUTION:

I'll go step-by-step so you can see what's happening. Multiply both sides by (w+2). This will 
clear the denominator on left side,





Now multiply both sides by (w-12). This will clear denominator on the right side.



Now use the distributive property to multiply all the factors out to polynomial form.


Combine like terms and rearrange by descending degree on both sides.


This is a quadratic equation. We need to set it equal to zero to solve. Rewrite as an equivalent 
equation with all terms on the left.


I always try to factor first because it's faster than the quadratic formula.
factors of 2w^2 are 2w and w.
factors of 24 are positive/positive or negative/negative
24 and 1, 
12 and 2, 
8 and 3,
6 and 4

We want a combination that sums to -19x when we distribute. The factors -8 and -3 will
work because (-8)(2x)+(-3(x)=-19x.

Write the quadratic equation in factored form.


By the Zero Product Property, either

 OR 

Therefore, our solutions are x = 1.5 or x = 8.

Check you work by substituting these values into the original equation.

For x = 8:



 CHECK!

For x=1.5:



 CHECK!

Hope this helps! Feel free to email if you have any questions.

Mrs. Figgy
math.in.the.vortex@gmail.com