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Sagot :
The expression which is equivalent to the provided complex fraction is equal to the expression,
[tex]{\dfrac{-4x+7}{2(x-2)}}[/tex]
What is the equivalent expression?
Equivalent expressions are the expression whose result is equal to the original expression, but the way of representation is different.
The expression given in the problem is,
[tex]\dfrac{\dfrac{3}{x-1}-4}{2-\dfrac{2}{x-1}}[/tex]
Let the expression which is equivalent to the above expression is f(x). Therefore,
[tex]f(x)=\dfrac{\dfrac{3}{x-1}-4}{2-\dfrac{2}{x-1}}[/tex]
Take the LCM (x-1) in the numerator and denominator as,
[tex]f(x)=\dfrac{\dfrac{3-4(x-1)}{x-1}}{\dfrac{2(x-1)-2}{x-1}}[/tex]
Simplify the expression and cancel out the (x-1) from both the fraction as,
[tex]f(x)={\dfrac{3-4(x-1)}{2(x-1)-2}}\\f(x)={\dfrac{3-4x+4}{2x-2-2}}\\f(x)={\dfrac{-4x+7}{2(x-2)}}[/tex]
Hence, the expression which is equivalent to the provided complex fraction is equal to the expression,
[tex]{\dfrac{-4x+7}{2(x-2)}}[/tex]
Learn more about the equivalent expression here;
https://brainly.com/question/2972832
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