QuestionFind the value of $\frac{2 x-2}{3-3 x}$ for $x \neq 1$ . Choose from: a. -1 b. $\frac{2}{3}$ c. $-\frac{2}{3}$ d. $-\frac{2}{3 x}$ .

Studdy Solution

STEP 1

Assumptions1. The given expression is $\frac{x -}{3 -3x}$ . The value of $x$ is not equal to $1$ .

STEP 2

We can simplify the given expression by factoring out common factors in the numerator and the denominator.
In the numerator, we can factor out a $2$ from $2x -2$ to get $2(x -1)$ .
In the denominator, we can factor out a $$ from $ -x$ to get $(1 - x)$.
So, the expression becomes $\frac{2(x -1)}{(1 - x)}$

STEP 3

We can simplify the expression further by noting that $x -1$ is the same as $-(1 - x)$ .So, the expression becomes $\frac{2(-(1 - x))}{3(1 - x)}$

STEP 4

The $(1 - x)$ terms in the numerator and the denominator cancel out, leaving us with $- \frac{2}{3}$ Therefore, the simplified form of the given expression is $- \frac{2}{3}$ .
So, the correct answer is (c) $- \frac{2}{3}$ .

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