Simplify the following into a single expression
x^3/(x^2-1)^5/8 + 2x(x^2-1)^3/8
write it as:
x^3(x^2-1)^(-5/8) + 2x(x^2-1)^3/8
common factor is x(x^2 - 1)^(-5/8)
so we get
=x(x^2 - 1)^(-5/8) [ x^2 + 2(x^2 - 1)]
= x(x^2 - 1)^(-5/8) (3x^2 - 2)
or
= x(3x^2 - 2)/(x(x^2 - 1)^(5/8) )
Thanks and thanks for the help on how to write it out on the computer.
You are welcome
To simplify the given expression, you need to simplify each term individually and then combine them.
Let's start with the first term: x^3/(x^2-1)^5/8.
Step 1: Rewrite the term with rational exponents:
x^(3/1) / (x^2-1)^(5/8).
Step 2: Simplify the numerator:
x^(3/1) is equal to x^3.
Step 3: Simplify the denominator:
The denominator (x^2-1)^(5/8) cannot be further simplified.
Now let's simplify the second term: 2x(x^2-1)^3/8.
Step 1: Distribute the 2x to both terms inside the parentheses:
2x * (x^2)^3 * (-1)^3 / 8.
Step 2: Simplify the numerator:
2x * x^6 * (-1) / 8.
Step 3: Combine like terms:
-2x^7 / 8.
Now we can combine both terms by adding them together:
x^3/(x^2-1)^(5/8) - 2x^7/8.
This gives us the simplified expression.