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Question Simplify given expressions. Click "Cannot be simplified" if applicable. 2y−55−2y=□\frac{2y-5}{5-2y}=\square and −6+yy−6=□\frac{-6+y}{y-6}=\square

Studdy Solution

STEP 1

Assumptions
1. We are given two rational expressions: 2y−55−2y\frac{2y-5}{5-2y} and −6+yy−6\frac{-6+y}{y-6}.
2. We need to simplify these expressions if possible.

STEP 2

Let's start with the first expression 2y−55−2y\frac{2y-5}{5-2y}. Notice that the numerator and the denominator are similar but with opposite signs. We can factor out a negative sign from one of them to make them look more alike.

STEP 3

Factor out −1-1 from the denominator to match the numerator.
2y−55−2y=2y−5−(2y−5)\frac{2y-5}{5-2y} = \frac{2y-5}{-(2y-5)}

STEP 4

Now that the numerator and denominator are the same except for the negative sign, they cancel each other out, leaving us with just the negative sign.
2y−5−(2y−5)=−1\frac{2y-5}{-(2y-5)} = -1

STEP 5

So the simplified form of the first expression is −1-1.

STEP 6

Now let's move on to the second expression −6+yy−6\frac{-6+y}{y-6}. Similar to the first expression, we can reorder the terms in the numerator to match the denominator.

STEP 7

Reorder the terms in the numerator.
−6+yy−6=y−6y−6\frac{-6+y}{y-6} = \frac{y-6}{y-6}

STEP 8

Now that the numerator and the denominator are exactly the same, they cancel each other out.
y−6y−6=1\frac{y-6}{y-6} = 1

STEP 9

So the simplified form of the second expression is 11.
The simplified forms of the given expressions are: 2y−55−2y=−1−6+yy−6=1 \begin{array}{l} \frac{2 y-5}{5-2 y} = -1 \\ \frac{-6+y}{y-6} = 1 \end{array}

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