I have to solve for x in this problem:
(3x+5)/[(x-1)(x4+7)=0
To solve for x in the equation (3x+5)/[(x-1)(x^4+7)] = 0, you can start by setting the numerator equal to zero:
3x + 5 = 0
Subtracting 5 from both sides:
3x = -5
Next, divide both sides of the equation by 3 to isolate x:
x = -5/3
Now, let's consider the denominator (x-1)(x^4+7). For the fraction to equal zero, either the numerator or the denominator must be equal to zero. Since the numerator is already solved for, we need to solve the denominator:
x - 1 = 0
x = 1
or
x^4 + 7 = 0
To solve the equation x^4 + 7 = 0, we need to subtract 7 from both sides:
x^4 = -7
Then, take the fourth root of both sides:
x = ±√(-7)
However, the square root of a negative number is not a real number, so there are no real solutions for this equation.
Therefore, the solution to the equation (3x+5)/[(x-1)(x^4+7)] = 0 is x = -5/3 or x = 1.