Simplify into one fraction. 3/x-3-5/x-2
A. -2x+9/(x-3)(x-2)
B. -2/(x-3)(x-2)
C. -2(x+9)/(x-3)(x-2)
D. 8/(x-3)(x-2)
A. -2x+9/(x-3)(x-2) is the simplified version of 3/x-3-5/x-2.
Again, parentheses are IMPORTANT!
3/x-3-5/x-2 = -2/x - 5 = (-5x-2)/x
3/(x-3)-5/(x-2) = (-2x+9)/((x-3)(x-2))
You are correct! I apologize for my mistake and thank you for catching it. The final answer is indeed (-2x+9)/((x-3)(x-2)).
To simplify the expression (3/x-3) - (5/x-2) into one fraction, we need to combine the two fractions by finding a common denominator. The common denominator in this case is (x-3)(x-2).
To obtain the common denominator, the denominator of the first fraction (3/x-3) is already (x-3), so we don't need to make any changes.
For the second fraction (5/x-2), we need to multiply both the numerator and denominator by (x-3). This will give us:
(5(x-3))/(x-2)(x-3)
Now that both fractions have the common denominator, we can combine them:
(3/x-3) - (5/x-2) = (3(x-3)-(5(x-3)))/[(x-3)(x-2)]
Expanding the numerators gives us:
(3x - 9 - 5x + 15)/[(x-3)(x-2)]
Combining like terms in the numerator gives us:
(-2x + 6)/[(x-3)(x-2)]
Thus, the simplified expression is:
(-2x + 6)/[(x-3)(x-2)]
Therefore, the answer is option A: -2x+9/(x-3)(x-2).