Could you please check my answer to this problem:

Simplify the expression

Original problem:
(3x^2+10x-8)/(3x^2-17x+10) x

(2x^2 + 9x -5)/(x^2 + 3x-4)

The answer I got was:

(3x +4)(x-2)/ (3x-2)(x-5)

x (2x-1) ( x +5)/ (x +4) (x-1)

so basically the problem could not be simplified more:
Is this right

Thank you

disagree about first factors

(3x-2)(x+4)(2x-1)(x+5)
----------------------
(3x-2)(x-5)(x+4)(x-1)

note x+4 top and bottom

To check if your answer is correct, let's simplify both expressions and compare them.

Original problem:
(3x^2+10x-8)/(3x^2-17x+10) x
(2x^2 + 9x -5)/(x^2 + 3x-4)

Let's factor both numerator and denominator separately.

Factoring the numerator of the first expression:
3x^2 + 10x - 8

The factors of 3x^2 are (3x, x).
The factors of -8 are (-2, 4) or (-4, 2).
Trying different combinations, we find that (3x + 4)(x - 2) is the correct factoring.
So the numerator of the first expression can be written as (3x + 4)(x - 2).

Factoring the denominator of the first expression:
3x^2 - 17x + 10

The factors of 3x^2 are (3x, x).
The factors of 10 are (10, 1) or (-10, -1).
Trying different combinations, we find that (3x - 2)(x - 5) is the correct factoring.
So the denominator of the first expression can be written as (3x - 2)(x - 5).

Therefore, the first expression can be simplified as (3x + 4)(x - 2) / (3x - 2)(x - 5).

Now let's simplify the second expression.

Factoring the numerator of the second expression:
2x^2 + 9x - 5

The factors of 2x^2 are (2x, x).
The factors of -5 are (-5, 1) or (5, -1).
Trying different combinations, we find that (2x - 1)(x + 5) is the correct factoring.
So the numerator of the second expression can be written as (2x - 1)(x + 5).

Factoring the denominator of the second expression:
x^2 + 3x - 4

The factors of x^2 are (x, x).
The factors of -4 are (-4, 1) or (4, -1).
Trying different combinations, we find that (x + 4)(x - 1) is the correct factoring.
So the denominator of the second expression can be written as (x + 4)(x - 1).

Therefore, the second expression can be simplified as (2x - 1)(x + 5) / (x + 4)(x - 1).

Comparing the simplified forms of both expressions, we get:

(3x + 4)(x - 2) / (3x - 2)(x - 5)
(2x - 1)(x + 5) / (x + 4)(x - 1)

Your answer of (3x + 4)(x - 2) / (3x - 2)(x - 5) is correct.

For the second expression, you mentioned that you got x (2x-1) (x +5) / (x +4) (x-1), which simplifies to (2x - 1)(x + 5) / (x + 4)(x - 1). This is also correct.

In conclusion, both of your simplified expressions are correct, and the problem cannot be simplified further.

Well done! I hope this explanation helps.