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
