At Westonci.ca, we make it easy for you to get the answers you need from a community of knowledgeable individuals. 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 :
Alright, let's go through both parts of the problem step-by-step.
### Problem 18: Simplification
We need to simplify the expression:
[tex]\[ \frac{1 - 5x}{1 - 5x} \][/tex]
1. Observe that the numerator and the denominator are the same:
[tex]\[ 1 - 5x \][/tex]
2. Since any non-zero number divided by itself equals 1, we can simplify this fraction directly:
[tex]\[ \frac{1 - 5x}{1 - 5x} = 1 \][/tex]
Thus, the simplified form of the expression is:
[tex]\[ 1 \][/tex]
### Problem 20: Solving the Equation
We are given this equation to solve for [tex]\( x \)[/tex]:
[tex]\[ \frac{(x+1)(x+2)}{(x+11)(x-2)} = 1 \][/tex]
To solve this equation, let's follow these steps:
1. Cross-multiply to eliminate the fraction:
[tex]\[ (x + 1)(x + 2) = (x + 11)(x - 2) \][/tex]
2. Expand both sides of the equation:
[tex]\[ x^2 + 3x + 2 = x^2 + 9x - 22 \][/tex]
3. Subtract [tex]\( x^2 \)[/tex] from both sides to eliminate the quadratic term:
[tex]\[ 3x + 2 = 9x - 22 \][/tex]
4. Rearrange the equation to isolate [tex]\( x \)[/tex]:
[tex]\[ 2 + 22 = 9x - 3x \][/tex]
[tex]\[ 24 = 6x \][/tex]
5. Solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{24}{6} = 4 \][/tex]
Thus, the solution to the equation is:
[tex]\[ x = 4 \][/tex]
### Summary
1. The simplified form of the expression [tex]\(\frac{1 - 5x}{1 - 5x}\)[/tex] is [tex]\( 1 \)[/tex].
2. The solution to the equation [tex]\(\frac{(x+1)(x+2)}{(x+11)(x-2)} = 1\)[/tex] is [tex]\( x = 4 \)[/tex].
### Problem 18: Simplification
We need to simplify the expression:
[tex]\[ \frac{1 - 5x}{1 - 5x} \][/tex]
1. Observe that the numerator and the denominator are the same:
[tex]\[ 1 - 5x \][/tex]
2. Since any non-zero number divided by itself equals 1, we can simplify this fraction directly:
[tex]\[ \frac{1 - 5x}{1 - 5x} = 1 \][/tex]
Thus, the simplified form of the expression is:
[tex]\[ 1 \][/tex]
### Problem 20: Solving the Equation
We are given this equation to solve for [tex]\( x \)[/tex]:
[tex]\[ \frac{(x+1)(x+2)}{(x+11)(x-2)} = 1 \][/tex]
To solve this equation, let's follow these steps:
1. Cross-multiply to eliminate the fraction:
[tex]\[ (x + 1)(x + 2) = (x + 11)(x - 2) \][/tex]
2. Expand both sides of the equation:
[tex]\[ x^2 + 3x + 2 = x^2 + 9x - 22 \][/tex]
3. Subtract [tex]\( x^2 \)[/tex] from both sides to eliminate the quadratic term:
[tex]\[ 3x + 2 = 9x - 22 \][/tex]
4. Rearrange the equation to isolate [tex]\( x \)[/tex]:
[tex]\[ 2 + 22 = 9x - 3x \][/tex]
[tex]\[ 24 = 6x \][/tex]
5. Solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{24}{6} = 4 \][/tex]
Thus, the solution to the equation is:
[tex]\[ x = 4 \][/tex]
### Summary
1. The simplified form of the expression [tex]\(\frac{1 - 5x}{1 - 5x}\)[/tex] is [tex]\( 1 \)[/tex].
2. The solution to the equation [tex]\(\frac{(x+1)(x+2)}{(x+11)(x-2)} = 1\)[/tex] is [tex]\( x = 4 \)[/tex].
Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.
