Solve for x: (3x+5)/((x-1)(x^4+7))
You have written an algebraic expression, but not an equation.
You cannot "solve for x" without an equation
the sum of 11 and the product of 2 and a number r?
To solve for x in the expression (3x+5)/((x-1)(x^4+7)), we need to find the values of x that make the expression equal to zero.
First, let's take a look at the denominator: (x-1)(x^4+7).
For the expression to be defined, neither the terms (x-1) nor (x^4+7) can be equal to zero.
Setting each factor equal to zero and solving for x, we get:
x - 1 = 0
x = 1
x^4 + 7 = 0
There is no real value for x that satisfies this equation since x^4 + 7 is always greater than zero for any real number x.
So, our denominator (x-1)(x^4+7) can never be zero.
Now, let's consider the numerator (3x + 5).
We need to solve the equation (3x + 5) = 0 to find the values of x that make the entire expression equal to zero.
Subtracting 5 from both sides:
3x = -5
Dividing both sides by 3:
x = -5/3
Therefore, the value of x that makes the expression (3x+5)/((x-1)(x^4+7)) equal to zero is x = -5/3.