((2x)/(x-1)) - (9/(x-2))
Is the answer (2x^2 - 13x + 9)/(x^2 - 3x + 2), or can it be simplified further?
I got an answer to this question before, but it seems like they did it with 9x instead of 9.
I agree with you.
correct
To simplify the expression ((2x)/(x-1)) - (9/(x-2)), we need to combine the fractions into a single fraction by finding a common denominator. The common denominator will be (x-1)(x-2), as it includes both denominators: (x-1) and (x-2).
Let's begin by multiplying the first fraction, ((2x)/(x-1)), by (x-2)/(x-2). This will eliminate the fraction in the denominator:
((2x)/(x-1)) * (x-2)/(x-2) = (2x(x-2))/((x-1)(x-2))
Next, let's multiply the second fraction, (9/(x-2)), by (x-1)/(x-1). This will eliminate the fraction in the denominator:
(9/(x-2)) * (x-1)/(x-1) = (9(x-1))/((x-1)(x-2))
Now, we can subtract the fractions:
((2x(x-2))/((x-1)(x-2))) - ((9(x-1))/((x-1)(x-2)))
To simplify further, we can expand and combine like terms in the numerator:
(2x(x-2) - 9(x-1))/((x-1)(x-2))
Multiplying, we get:
(2x^2 - 4x - 9x + 9)/((x-1)(x-2))
Combining like terms, we have:
(2x^2 - 13x + 9)/((x-1)(x-2))
So, the simplified answer is (2x^2 - 13x + 9)/((x-1)(x-2)).
It seems like the previous answer you encountered might have made a mistake by multiplying 9 by x instead of just 9.