Welcome to Westonci.ca, your go-to destination for finding answers to all your questions. Join our expert community today! Ask your questions and receive precise answers from experienced professionals across different disciplines. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.
Sagot :
To find which expression is equivalent to [tex]\(\frac{\frac{3}{x-2}-5}{2-\frac{4}{x-2}}\)[/tex], we need to simplify the given expression step by step.
Given expression:
[tex]\[ \frac{\frac{3}{x-2}-5}{2-\frac{4}{x-2}} \][/tex]
### Step 1: Simplify the Numerator
First, we will simplify the numerator [tex]\(\frac{3}{x-2} - 5\)[/tex].
Rewrite [tex]\( -5 \)[/tex] as a fraction:
[tex]\[ -5 = \frac{-5(x-2)}{x-2} = \frac{-5x + 10}{x-2} \][/tex]
Now, combine the fractions:
[tex]\[ \frac{3}{x-2} - 5 = \frac{3}{x-2} + \frac{-5x + 10}{x-2} = \frac{3 - 5x + 10}{x-2} = \frac{13 - 5x}{x-2} \][/tex]
### Step 2: Simplify the Denominator
Next, we need to simplify the denominator [tex]\( 2 - \frac{4}{x-2} \)[/tex].
Rewrite [tex]\( 2 \)[/tex] as a fraction:
[tex]\[ 2 = \frac{2(x-2)}{x-2} = \frac{2x - 4}{x-2} \][/tex]
Now, combine the fractions:
[tex]\[ 2 - \frac{4}{x-2} = \frac{2x - 4}{x-2} - \frac{4}{x-2} = \frac{2x - 4 - 4}{x-2} = \frac{2x - 8}{x-2} \][/tex]
### Step 3: Divide the Numerator by the Denominator
Now that we have simplified both the numerator and the denominator, we can divide one by the other:
[tex]\[ \frac{\frac{13 - 5x}{x-2}}{\frac{2x - 8}{x-2}} \][/tex]
Since both fractions have the same denominator [tex]\((x-2)\)[/tex], they cancel out:
[tex]\[ \frac{13 - 5x}{2x - 8} \][/tex]
### Simplified Expression
The equivalent simplified expression is:
[tex]\[ \frac{13 - 5x}{2x - 8} \][/tex]
Thus, the correct answer is:
[tex]\[ \boxed{\frac{13-5x}{2x-8}} \][/tex]
Given expression:
[tex]\[ \frac{\frac{3}{x-2}-5}{2-\frac{4}{x-2}} \][/tex]
### Step 1: Simplify the Numerator
First, we will simplify the numerator [tex]\(\frac{3}{x-2} - 5\)[/tex].
Rewrite [tex]\( -5 \)[/tex] as a fraction:
[tex]\[ -5 = \frac{-5(x-2)}{x-2} = \frac{-5x + 10}{x-2} \][/tex]
Now, combine the fractions:
[tex]\[ \frac{3}{x-2} - 5 = \frac{3}{x-2} + \frac{-5x + 10}{x-2} = \frac{3 - 5x + 10}{x-2} = \frac{13 - 5x}{x-2} \][/tex]
### Step 2: Simplify the Denominator
Next, we need to simplify the denominator [tex]\( 2 - \frac{4}{x-2} \)[/tex].
Rewrite [tex]\( 2 \)[/tex] as a fraction:
[tex]\[ 2 = \frac{2(x-2)}{x-2} = \frac{2x - 4}{x-2} \][/tex]
Now, combine the fractions:
[tex]\[ 2 - \frac{4}{x-2} = \frac{2x - 4}{x-2} - \frac{4}{x-2} = \frac{2x - 4 - 4}{x-2} = \frac{2x - 8}{x-2} \][/tex]
### Step 3: Divide the Numerator by the Denominator
Now that we have simplified both the numerator and the denominator, we can divide one by the other:
[tex]\[ \frac{\frac{13 - 5x}{x-2}}{\frac{2x - 8}{x-2}} \][/tex]
Since both fractions have the same denominator [tex]\((x-2)\)[/tex], they cancel out:
[tex]\[ \frac{13 - 5x}{2x - 8} \][/tex]
### Simplified Expression
The equivalent simplified expression is:
[tex]\[ \frac{13 - 5x}{2x - 8} \][/tex]
Thus, the correct answer is:
[tex]\[ \boxed{\frac{13-5x}{2x-8}} \][/tex]
We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.