Final answer:
To reduce the expression 1/x² +6x+8-1/ x² +3x-4, find the common denominator and combine the fractions. Simplify the expression and solve for x.
Step-by-step explanation:
To reduce the expression 1/x² +6x+8-1/ x² +3x-4 to its lowest form, we need to find the common denominator and combine the fractions.
The common denominator for x² and x² +3x-4 is x²(x² +3x-4).
Expanding the expression and multiplying both sides by the common denominator, we get: x²(x² +3x-4)/(x²(x² +3x-4)) = 1/x² +6x+8-1/(x² +3x-4).
Simplifying further, we have: x²(x² +3x-4) - 1 = 6x(x² +3x-4).
Now, we can solve for x by factoring or using the quadratic formula.