Get detailed and reliable answers to your questions on IDNLearn.com. Our experts provide prompt and accurate answers to help you make informed decisions on any topic.
Sagot :
Sure, let's solve and simplify the given expression step-by-step.
Given the expression:
[tex]\[ \frac{2x - 1 - 4ax + 2a}{2x^2 - x} \][/tex]
First, we'll simplify the numerator and the denominator separately where possible.
### Step 1: Simplify the numerator
The numerator is:
[tex]\[ 2x - 1 - 4ax + 2a \][/tex]
Group the terms involving [tex]\(x\)[/tex] together in the numerator:
[tex]\[ (2x - 4ax) + (-1 + 2a) \][/tex]
Factor [tex]\(x\)[/tex] out from the first group:
[tex]\[ 2x(1 - 2a) + (-1 + 2a) \][/tex]
So, the numerator simplifies to:
[tex]\[ 2x(1 - 2a) + (-1 + 2a) \][/tex]
### Step 2: Simplify the denominator
The denominator is:
[tex]\[ 2x^2 - x \][/tex]
Factor out [tex]\(x\)[/tex] from the denominator:
[tex]\[ x(2x - 1) \][/tex]
### Step 3: Combine and simplify the expression
Putting the simplified numerator and denominator together:
[tex]\[ \frac{2x(1 - 2a) + (-1 + 2a)}{x(2x - 1)} \][/tex]
To simplify this expression, we need to separate the terms in the numerator and then try to cancel common factors. Split the fraction:
[tex]\[ = \frac{2x(1 - 2a)}{x(2x - 1)} + \frac{-1 + 2a}{x(2x - 1)} \][/tex]
We can cancel [tex]\(x\)[/tex] in the first term of the numerator and the denominator:
[tex]\[ = \frac{2(1 - 2a)}{2x - 1} + \frac{-1 + 2a}{x(2x - 1)} \][/tex]
Now observe that both parts individually do not share any further common factors, thus the final simplified version of the expression is:
[tex]\[ \frac{1 - 2a}{x} \][/tex]
Hence, the expression simplifies to:
[tex]\[ \frac{1 - 2a}{x} \][/tex]
Given the expression:
[tex]\[ \frac{2x - 1 - 4ax + 2a}{2x^2 - x} \][/tex]
First, we'll simplify the numerator and the denominator separately where possible.
### Step 1: Simplify the numerator
The numerator is:
[tex]\[ 2x - 1 - 4ax + 2a \][/tex]
Group the terms involving [tex]\(x\)[/tex] together in the numerator:
[tex]\[ (2x - 4ax) + (-1 + 2a) \][/tex]
Factor [tex]\(x\)[/tex] out from the first group:
[tex]\[ 2x(1 - 2a) + (-1 + 2a) \][/tex]
So, the numerator simplifies to:
[tex]\[ 2x(1 - 2a) + (-1 + 2a) \][/tex]
### Step 2: Simplify the denominator
The denominator is:
[tex]\[ 2x^2 - x \][/tex]
Factor out [tex]\(x\)[/tex] from the denominator:
[tex]\[ x(2x - 1) \][/tex]
### Step 3: Combine and simplify the expression
Putting the simplified numerator and denominator together:
[tex]\[ \frac{2x(1 - 2a) + (-1 + 2a)}{x(2x - 1)} \][/tex]
To simplify this expression, we need to separate the terms in the numerator and then try to cancel common factors. Split the fraction:
[tex]\[ = \frac{2x(1 - 2a)}{x(2x - 1)} + \frac{-1 + 2a}{x(2x - 1)} \][/tex]
We can cancel [tex]\(x\)[/tex] in the first term of the numerator and the denominator:
[tex]\[ = \frac{2(1 - 2a)}{2x - 1} + \frac{-1 + 2a}{x(2x - 1)} \][/tex]
Now observe that both parts individually do not share any further common factors, thus the final simplified version of the expression is:
[tex]\[ \frac{1 - 2a}{x} \][/tex]
Hence, the expression simplifies to:
[tex]\[ \frac{1 - 2a}{x} \][/tex]
Your participation means a lot to us. Keep sharing information and solutions. This community grows thanks to the amazing contributions from members like you. IDNLearn.com has the solutions to your questions. Thanks for stopping by, and see you next time for more reliable information.