((2x)/(x-1)) - (9/(x-2))
Is the answer (2x^2 - 13x + 9)/(x^2 - 3x + 2), or can it be simplified further?
2 x / ( x - 1 ) - 9 x / ( x - 2 ) =
[ 2 x ( x - 2 ) - 9 x ( x - 1 ) ] / [ ( x - 1 ) ( x - 2 ) ] =
[ 2 x * x + 2 x * ( - 2 ) - 9 x * x - 9 x * ( - 1 ) ] / ( x ^ 2 - 3 x + 2 ) =
( 2 x ^ 2 - 4 x - 9 x ^ 2 + 9 x ) / ( x ^ 2 - 3 x + 2 ) =
( - 7 x ^ 2 + 5 x ) / ( x ^ 2 - 3 x + 2 ) =
- ( 7 x ^ 2 - 5 x ) / ( x ^ 2 - 3 x + 2 ) =
- x ( 7 x - 5 ) / ( x ^ 2 - 3 x + 2 ) =
It is 9, not 9x.
To simplify the given expression, ((2x)/(x-1)) - (9/(x-2)), we need to find a common denominator for the two fractions and combine them.
The common denominator for (x-1) and (x-2) is (x-1)(x-2).
Let's rewrite both fractions with the common denominator:
((2x)/(x-1)) = (2x)(x-2)/[(x-1)(x-2)] = (2x^2 - 4x)/[(x-1)(x-2)]
(- 9/(x-2)) = -9(x-1)/[(x-1)(x-2)]
Now, we can combine the two fractions:
((2x)/(x-1)) - (9/(x-2)) = (2x^2 - 4x)/[(x-1)(x-2)] - 9(x-1)/[(x-1)(x-2)]
Since the denominators are the same, we can add the numerators:
= (2x^2 - 4x - 9x + 9)/[(x-1)(x-2)]
Combining like terms:
= (2x^2 - 13x + 9)/[(x-1)(x-2)]
The expression (2x^2 - 13x + 9)/(x^2 - 3x + 2) is the simplified form of the given expression. It cannot be further simplified.