Hi, there--

THE PROBLEM:
Solve for x.


A SOLUTION:
THis problem will be easier to solve if we clear the denominators from each term. Multiply
each side of the equation by (x-1)(x+1), the LCD (least common denominator.)



We can eliminate the common factors in the numerator and denominator because any 
non-zero expression divided by itself equals 1.


Simplify.


Use the distributive property to clear the parentheses.


This is a quadratic equation because the 4x-squared term has the highest degree. To solve it, 
set this equation equal to zero by moving all terms to the left side.



I always try to factor these first because I like factoring and the quadratic formula is not my 
friend! The quadratic formula will always work, though. Factoring, only sometimes.

Find the factors of x-squared term (-4x^2):
-4x,x
4,-x
2x,-2x

Find the factors of the constant term (4):
4,1
2,2

We are looking for a combination with a sum of the x-term (6x):
2x,-2x and 4,1 work because (2x)(4)+(-2x)(1) = 8x - 2x = 6x

Your equation in factored form is


Applying the Zero Product Property, we know that either 2x+1=0 or -2x+4=0. Solve these
equations.
2x + 1 = 0    --->  2x = -1  --->  x = -1/2
-2x + 4 = 0  --->  -2x = -4  --->  x = 2

The solutions to your equation are x=-1/2 or x=2.

Check these values in the original equation.


For x=-1/2:



CHECK!

For x=2:



CHECK!

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

Good luck with your math,

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