Which expression is equivalent to the following complex fraction? StartFraction 3 Over x minus 1 EndFraction minus 4 divided by

Question

2 years ago

7

2 minus StartFraction 2 Over x minus 1 EndFraction.

1 answer:

zimovet [89] · Answer 1 · 2022-12-14T09:20:05+03:00

The expression which is equivalent to the provided complex fraction is equal to the expression,

${\dfrac{-4x+7}{2(x-2)}}$

<h3>What is the equivalent expression?</h3>

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,

$\dfrac{\dfrac{3}{x-1}-4}{2-\dfrac{2}{x-1}}$

Let the expression which is equivalent to the above expression is f(<em>x</em>). Therefore,

$f(x)=\dfrac{\dfrac{3}{x-1}-4}{2-\dfrac{2}{x-1}}$

Take the LCM (x-1) in the numerator and denominator as,

$f(x)=\dfrac{\dfrac{3-4(x-1)}{x-1}}{\dfrac{2(x-1)-2}{x-1}}$

Simplify the expression and cancel out the (x-1) from both the fraction as,

$f(x)={\dfrac{3-4(x-1)}{2(x-1)-2}}\\f(x)={\dfrac{3-4x+4}{2x-2-2}}\\f(x)={\dfrac{-4x+7}{2(x-2)}}$

Hence, the expression which is equivalent to the provided complex fraction is equal to the expression,

${\dfrac{-4x+7}{2(x-2)}}$

Learn more about the equivalent expression here;