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18: Simplify [tex]\frac{1-5x}{1-5x}[/tex]

20: Solve [tex]\frac{(x+1)(x+2)}{(x+11)(x-2)}=1[/tex]


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].

A15nswer:

Step-by-step explanation: