[x^5(-3)(x^2+1)^-4(2x)]-(x^2+1)^-3(5)x^4] / (x^5)^2
Can someone show my how to simplify this, step by step? So far I got that the denominator should be x^10 because of the exponents, and (x^2+1)^-4 could be simplified as [(x+1)(x-1)]/4, likewise with (x^2+1)^-3, except the denominator is 3. Help please! Thanks much!
The way you wrote your expression is very confusing,
e.g. in [x^5(-3)(x^2+1)^-4(2x)]
is that [x^(-15) * (x^2+1)^(-8x)] ?
or [-3x^5 * 2x/(x^2+1)^4] ?
You said (x^2+1)^-4 could be simplified as [(x+1)(x-1)]/4
this is false, x^2 + 1 does NOT factor to ((x+1)(x-1)
PLease use some more brackets, or some other way, to properly state your expression.
sorry about that. it was written like that in the book o.o''
It should be this (I think):
[x^5*(-3)*[(x^2+1)^-4]*(2x)]
- {[(x^2+1)^-3] * [(5)x^4]}
over (x^5)^2
[x^5*(-3)*[(x^2+1)^-4]*(2x)]-{[(x^2+1)^-3]*[(5)x^4]} / [ (x^5)^2 ] =
{(-3)*(2x)*(x^5)*[(x^2+1)^-4]}-{(5)+(x^4)*[((x^2)+1)^-3] / (x^7) =
(-6)*(x^6)*[((x^2)+1)^-4]-{(5)*(x^4)*[(x^2+1)^-3] / (x^7) =
{[(-6)*(x^6)*[((x^2)+1)^-4]]/x^7}-[{(5)*(x^4)*[(x^2+1)^-3] /(x^7)] =
{[(-6)*[((x^2)+1)^-4]]/x}-[(5)*[(x^2+1)^-3] /(x^3)] =
(6/(x)[((x^2)+1)^4})] - (5/(x^3)[((X^2)+1)^3]
i think
To simplify this expression step by step, let's start by expanding the given expression:
[x^5(-3)(x^2+1)^-4(2x)] - [(x^2+1)^-3(5)x^4] / (x^5)^2
1. First, let's simplify the expressions within the square brackets separately.
a) For x^5(-3)(x^2+1)^-4(2x):
- Distribute x^5 and 2x across the terms inside (x^2+1)^-4:
x^5 * (-3) * 2x * [(x^2+1)^-4]
- Combine the x terms and simplify the exponent:
-6x^2(x^2+1)^-4
b) For (x^2+1)^-3(5)x^4:
- Simplify the exponent and distribute:
5x^4 * (x^2+1)^-3
Now, the expression becomes:
[-6x^2(x^2+1)^-4] - [5x^4(x^2+1)^-3] / (x^5)^2
2. Next, let's simplify the denominators (x^2+1)^-4 and (x^2+1)^-3:
- The reciprocal of (x^2+1)^-4 is (x^2+1)^4.
- The reciprocal of (x^2+1)^-3 is (x^2+1)^3.
Now, the expression becomes:
[-6x^2 / (x^2+1)^4] - [5x^4 / (x^2+1)^3] / (x^5)^2
3. To simplify the numerator, we need to find a common denominator:
- Find the least common denominator between (x^2+1)^4 and (x^2+1)^3, which is (x^2+1)^4.
Now, the expression becomes:
[-6x^2 - (5x^4(x^2+1)) / (x^2+1)^4] / (x^5)^2
4. Simplify the numerator further:
- Distribute 5x^4 across (x^2+1):
-6x^2 - 5x^6 - 5x^4 / (x^2+1)^4
5. Simplify the denominator:
- Expand (x^5)^2 as x^(5*2) = x^10.
Now, the expression becomes:
[-6x^2 - 5x^6 - 5x^4] / (x^2+1)^4x^10
This is the final simplified form of the given expression.