To solve this problem, we need to solve for x in the first equation, then substitute in this value for x into the second equation.
Let's begin by starting to solve for x in the first equation, x-1/x = 5. To begin, we should multiply both sides of the equation by x to get rid of the denominator on the left side of the equation.
x-1/x = 5
x-1 = 5x
Then, we should subtract x from both sides of the equation so that all of the variables are on the right side of the equation.
-1 = 4x
Finally, we can divide both sides of the equation by 4, to get the variable x alone on the right side.
x = -1/4
Now, we should substitute in this value of x into the second equation.
x^3 + 1 / x^3
(-1/4)^3 + 1 / (-1/4)^3
To simplify, we can begin by simplifying the exponents.
-1/64 + 1 / -1/64
Next, we should change 1 into 64/64 so that we can simplify the numerator of the fraction.
-1/64 + 64/64 / -1/64
To simplify, we need to add the two fractions in the numerator.
63/64 / -1/64
Because both of the "individual" fractions of the numerator and denominator have the common denominator of 64, we can get rid of the both of the denominators, as follows:
63/-1
Finally, we can perform this simple division.
-63
Therefore, your answer is -63.
Hope this helps!
