Solved on Jan 24, 2024

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

STEP 1

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

STEP 2

Let's start with the first expression $\frac{2y-5}{5-2y}$ . 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 $-1$ from the denominator to match the numerator.
$\frac{2y-5}{5-2y} = \frac{2y-5}{-(2y-5)}$

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.
$\frac{2y-5}{-(2y-5)} = -1$

STEP 5

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

STEP 6

Now let's move on to the second expression $\frac{-6+y}{y-6}$ . 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.
$\frac{-6+y}{y-6} = \frac{y-6}{y-6}$

STEP 8

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

STEP 9

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

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

STEP 1

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

STEP 2

Let's start with the first expression $\frac{2y-5}{5-2y}$ . 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 $-1$ from the denominator to match the numerator.
$\frac{2y-5}{5-2y} = \frac{2y-5}{-(2y-5)}$

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.
$\frac{2y-5}{-(2y-5)} = -1$

STEP 5

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

STEP 6

Now let's move on to the second expression $\frac{-6+y}{y-6}$ . 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.
$\frac{-6+y}{y-6} = \frac{y-6}{y-6}$

STEP 8

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

STEP 9

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

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Simplify given expressions. Click "Cannot be simplified" if applicable. 2y−55−2y=□\frac{2y-5}{5-2y}=\square5−2y2y−5​=□ and −6+yy−6=□\frac{-6+y}{y-6}=\squarey−6−6+y​=□

STEP 1

Assumptions1. We are given two rational expressions: 2y−55−2y\frac{2y-5}{5-2y}5−2y2y−5​ and −6+yy−6\frac{-6+y}{y-6}y−6−6+y​.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}5−2y2y−5​. 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 −1-1−1 from the denominator to match the numerator.2y−55−2y=2y−5−(2y−5)\frac{2y-5}{5-2y} = \frac{2y-5}{-(2y-5)}5−2y2y−5​=−(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−(2y−5)2y−5​=−1

STEP 5

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

STEP 6

Now let's move on to the second expression −6+yy−6\frac{-6+y}{y-6}y−6−6+y​. 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}y−6−6+y​=y−6y−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} = 1y−6y−6​=1

STEP 9

So the simplified form of the second expression is 111.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} 5−2y2y−5​=−1y−6−6+y​=1​

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

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

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

Let's start with the first expression $\frac{2y-5}{5-2y}$ . 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.

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

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.
$\frac{2y-5}{-(2y-5)} = -1$

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

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

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

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

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