Answer:
[tex]\dfrac{7-4x}{-4+2x}[/tex]
Step-by-step explanation:
We have been given with the expression
[tex]\Rightarrow \dfrac{\dfrac{3}{x-1}-4}{2-\dfrac{2}{x-1}}[/tex]
Whenever we are asked the equivalent expression of any given expression it means we have to find the simplest form of the given expression.
Taking the LCM in numerator and denominator we will get
[tex]\Rightarrow \dfrac{\dfrac{3-4(x-1)}{x-1}}{\dfrac{2(x-1)-2}{x-1}}[/tex]
Now we will cancel the common factor from numerator and denominator which is (x-1) we will get
[tex]\frac{3-4(x-1)}{2(x-1)-2}[/tex] after opening the parenthesis we will get
[tex]\frac{3-4x+4}{2x-2-2}[/tex]
After simplifying numerator and denominator we will get
[tex]\frac{7-4x}{-4+2x}[/tex]
Given expression [tex]\dfrac{\dfrac{3}{x-1}-4}{2-\dfrac{2}{x-1}}[/tex] is equivalent to [tex]\dfrac{7-4x}{-4+2x}[/tex]
