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How do you simplify $\frac{2 x - 4 x}{x^{2} - 3 x + 2} \times \frac{x^{2} - 4 x}{4}$ ?
Sub Grade: 10

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\frac{x (x - 4)}{2 (x - 1)}

\frac{x (x - 5)}{2 (x - 2)}

\frac{x (x - 7)}{2 (x - 3)}

\frac{x (x - 3)}{2 (x - 4)}

answer is A.

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Detailed Solution

Given

\frac{2 x - 4 x}{x^{2} - 3 x + 2}

\times \frac{x^{2} - 4 x}{4}

Let the common factor of each term as explained below
⇒2x - 4 = 2 (x-2)
⇒x2 - 4x = x (x-4)
⇒x2- 3x+ 2 = x2 - 1x - 2x +2 = x(x- 1)- 2 (x-1)= (x-2)(x-1)
So now we have
⇒

\frac{2 (x - 2)}{(x - 2) (x - 1)} \times \frac{x (x - 4)}{4}

⇒

\frac{2 x - 2}{x - 2 (x - 1)} \times \frac{x (x - 4)}{4}

⇒

\frac{x (x - 4)}{2 (x - 1)}

Type Exam: CBSE

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