Simplify into one fraction.
3/(x-3)-5/(x-2)
• (-2x + 9)/(x-3)(x-2)
• (-2x)/(x-3)(x-2)
• (-2x -9)/(x-3)(x-2)
• (2x+9)/(x-3)(x-2)
How?
No problem, got this one.
Well what did you get
ugh you guys.., no answer really?
To simplify the expression (3/(x-3)) - (5/(x-2)) into one fraction, we need to find a common denominator for the two fractions.
The denominators of the two fractions are (x-3) and (x-2). To find the common denominator, we need to find the least common multiple (LCM) of the two denominators.
The LCM of (x-3) and (x-2) is (x-3)(x-2), as it is the smallest expression that both (x-3) and (x-2) divide into evenly.
Now, let's rewrite the fractions with the common denominator:
3/(x-3) - 5/(x-2) = (3(x-2))/[(x-3)(x-2)] - (5(x-3))/[(x-3)(x-2)]
Simplifying the numerators:
(3(x-2)) - (5(x-3)) = (3x - 6) - (5x - 15) = 3x - 6 - 5x + 15 = -2x + 9
Now, we have the numerator -2x + 9 and the common denominator (x-3)(x-2). So, the simplified expression is (-2x + 9)/[(x-3)(x-2)].
Therefore, the correct answer is A: (-2x + 9)/(x-3)(x-2).