To subtract and simplify the expression 2/x^2-2x - x/2x-4, we need to find a common denominator and combine the fractions.
The common denominator is (x^2-2x)(2x-4).
For the first fraction, we need to multiply the numerator and denominator by (2x-4) to obtain the common denominator:
2(2x-4)/(x^2-2x)(2x-4) = (4x-8)/(x^2-2x)(2x-4)
For the second fraction, we need to multiply the numerator and denominator by (x^2-2x) to obtain the common denominator:
x(x^2-2x)/(2x-4)(x^2-2x) = x(x^2-2x)/(x^2-2x)(2x-4)
Now, we can subtract the fractions:
(4x-8)/(x^2-2x)(2x-4) - x(x^2-2x)/(x^2-2x)(2x-4)
Combine the numerators:
(4x-8 - x(x^2-2x))/(x^2-2x)(2x-4)
Simplify the numerator:
(4x-8 - x^3 + 2x^2)/(x^2-2x)(2x-4)
Combine like terms:
(-x^3 + 2x^2 + 4x - 8)/(x^2-2x)(2x-4)
Now, the expression is simplified.
Subtract and simplify, make sure your answer is either an integer or a fraction. Show your work.
2/x^2-2x - x/2x-4
1 answer