How do you simplify and find the excluded value of #(x^2 – 3x + 2)/( 7x – 14) div(x^2 – 1)/(7x + 7)#?

Question

Savannah Anderson · Accepted Answer

Your expression simplifies to #1#, with restrictions being #x!=+-1, 2#.

Factor everything: #=>((x - 2)(x - 1))/(7(x - 2)) xx (7(x + 1))/((x + 1)(x - 1))# Cancel using the property #a/a = 1, a !=0#. #=>1# Now, state the restrictions on the variable. These will occur when the denominator equals #0#. #x!=-1, 1, 2# Hopefully this helps!

Kennedy Adams · Answer

undefined To simplify and find the excluded value of the expression (x^2 – 3x + 2)/(7x – 14) divided by (x^2 – 1)/(7x + 7), we can follow these steps:

1. Factorize the numerator and denominator of both fractions:
   (x^2 – 3x + 2) = (x – 1)(x – 2)
   (7x – 14) = 7(x – 2)
   (x^2 – 1) = (x – 1)(x + 1)
   (7x + 7) = 7(x + 1)

2. Rewrite the expression as a multiplication:
   [(x – 1)(x – 2)] / [7(x – 2)] * [7(x + 1)] / [(x – 1)(x + 1)]

3. Cancel out the common factors in the numerator and denominator:
   (x – 1) cancels out in the numerator and denominator.
   (x – 2) cancels out in the numerator and denominator.
   7 cancels out in the numerator and denominator.
   (x + 1) cancels out in the numerator and denominator.

4. Simplify the expression:
   The simplified expression is 1 / (x + 1).

5. Find the excluded value:
   The excluded value is the value of x that would make the denominator equal to zero. In this case, x cannot be -1, as it would result in division by zero.

Therefore, the simplified expression is 1 / (x + 1), and the excluded value is x = -1.