The problem is… 8X^4/25-9x^2• 3X^2- 8X+5/x^2-1~4x^3/x^2+2x+1
NOTE: I used~ to equal a division symbol
So I did 2x/-(3x-5)(5+3x)•3x(x-1)-5(x-1)/(x-1)(x+1)•(x+1)^2
2x/-(3x-5)(5+3x)•(x-1)(3x-5)/(x-1)(x+1)•(x+1)^2
2x/5+3x•-1(x+1)
-2x^2+2x/5+3x
Is this correct? Thank you for checking my work
Your use of upper- and lower-case X and weird symbols, combined with the lack of parentheses makes things very confusing and ambiguous.
Now, even though the formatting is garbled, you seem to be doing things right, till the last line, where you had
2x/5+3x•-1(x+1)
(-2x^2+2x)/(5+3x)
since you failed to distribute the - sign in 2x•-1(x+1) = 2x(-x-1) = -2x^2-2x
So, the final answer was
(-2x^2-2x)/(5+3x)
or, I would left it as
-2x(x+1)/(3x+5)
or
(-2x^2-2x)/(3x+5)
Thank you for your help.
To verify whether your simplification is correct, let's simplify the expression step by step:
First, let's simplify the expression:
8x^4 / 25 - 9x^2 * 3x^2 - 8x + 5 / x^2 - 1 ~ 4x^3 / x^2 + 2x + 1
Now, it seems there are a lot of terms and operations in the equation. We should simplify it further:
Simplifying the numerator:
8x^4 / 25 - (9x^2 * 3x^2) - 8x + 5 / x^2 - 1 ~ 4x^3 / x^2 + 2x + 1
8x^4 / 25 - (27x^4) - 8x + 5 / x^2 - 1 ~ 4x^3 / x^2 + 2x + 1
To simplify the expression involving division (~), we should keep in mind the order of operations. First, multiply and divide from left to right:
8x^4 / 25 - 27x^6 - 8x + 5 / x^2 - 1 ~ 4x^3 / x^2 + 2x + 1
Now, let's simplify the numerator:
(8x^4 - 27x^6 - 8x + 5) / (x^2 - 1) ~ 4x^3 / (x^2 + 2x + 1)
Next, let's factor the numerator:
(8x^4 - 27x^6 - 8x + 5) = (x - 1)(27x^5 + 27x^4 + 27x^3 + 27x^2 + 27x + 27) - 3x^3 - 3x^2 - 3x - 3
So the numerator becomes:
(8x^4 - 27x^6 - 8x + 5) = (x - 1)(27x^5 + 27x^4 + 27x^3 + 27x^2 + 27x + 27) - 3(x^3 + x^2 + x + 1)
Now, rewriting the expression:
((x - 1)(27x^5 + 27x^4 + 27x^3 + 27x^2 + 27x + 27) - 3(x^3 + x^2 + x + 1)) / (x^2 - 1) ~ 4x^3 / (x^2 + 2x + 1)
Simplifying the denominator:
(x^2 - 1) = (x - 1)(x + 1)
So the denominator becomes:
(x^2 - 1) = (x - 1)(x + 1)
Rewriting the whole expression:
((x - 1)(27x^5 + 27x^4 + 27x^3 + 27x^2 + 27x + 27) - 3(x^3 + x^2 + x + 1)) / ((x - 1)(x + 1)) ~ 4x^3 / (x^2 + 2x + 1)
Now, let's simplify the expression further:
Substituting the factored numerator and denominator:
((x - 1)(27x^5 + 27x^4 + 27x^3 + 27x^2 + 27x + 27) - 3(x^3 + x^2 + x + 1)) / ((x - 1)(x + 1)) ~ 4x^3 / (x^2 + 2x + 1)
Expanding the factored numerator:
(27x^6 + 27x^5 + 27x^4 + 27x^3 + 27x^2 + 27x - 27x^4 - 27x^3 - 27x^2 - 27x - 27 - 3x^3 - 3x^2 - 3x - 3) / ((x - 1)(x + 1)) ~ 4x^3 / (x^2 + 2x + 1)
Combine like terms:
27x^6 + 24x^5 - 3x^2 - 3 / ((x - 1)(x + 1)) ~ 4x^3 / (x^2 + 2x + 1)
Now, let's focus on the expression in the numerator:
4x^3 / (x^2 + 2x + 1)
We can factor the denominator:
(x^2 + 2x + 1) = (x + 1)(x + 1)
So the expression becomes:
4x^3 / (x + 1)(x + 1)
And that's our final expression.