The value of x is [tex]\mathbf{8\dfrac{1}{3}}[/tex]
The objective of this question is to evaluate and determine the value of x. The fraction given in the question consists of algebraic expressions and, we need to solve it through following process;
∴
[tex]\mathbf{\dfrac{x-1}{3-x} + \dfrac{3}{4}=-1 }[/tex]
Collect like terms
[tex]\mathbf{(\dfrac{x-1}{3-x})=-1 -\dfrac{3}{4}}}[/tex]
[tex]\mathbf{(\dfrac{x-1}{3-x})=-(\dfrac{7}{4}})}[/tex]
-4(x - 1) = -7(3 -x)
-4x + 4 = -21 + 7x
4x -7x = -21 - 4
-3x = - 25
[tex]\mathbf{x= \dfrac{25}{3}}[/tex]
[tex]\mathbf{x= 8\dfrac{1}{3}}[/tex]
Learn more about evaluating fractions here:
https://brainly.com/question/12023322
