Answer:
A. x = -37/14
B. x ≠ 9/2 or 1/3
Step-by-step explanation:
Given the rational equation 8/(2x -9) = 5/(3x -1), you want to know the solution and the restrictions on the variable.
Restrictions
The variable cannot take on any value that makes the equation undefined. The equation will be undefined if either denominator is zero, so we cannot have ...
2x -9 = 0 ⇒ x = 9/2
or
3x -1 = 0 ⇒ x = 1/3
The value of the variable may not be 1/3 or 9/2.
Solution
We can subtract the right side from both sides to get ...
[tex]\displaystyle \dfrac{8}{2x-9}=\dfrac{5}{3x-1}\qquad\text{given equation}\\\\\\\dfrac{8}{2x-9}-\dfrac{5}{3x-1}=0\qquad\text{subtract right side}\\\\\\\dfrac{8(3x-1)-5(2x-9)}{(2x-9)(3x-1)}=\dfrac{24x-8-10x+45}{(2x-9)(3x-1)}=0\\\\\\14x+37=0\qquad\text{numerator must be zero}\\\\\boxed{x=-\dfrac{37}{14}}\qquad\text{subtract 37, divide by 14}[/tex]
