Sure! Let's simplify the given algebraic expression step by step:
The expression we have is:
[tex]\[ \frac{-8x^2 + 2x - 1}{-2x} \][/tex]
We'll simplify the terms in the numerator by dividing each term by the denominator.
First, separate the numerator into three individual fractions:
[tex]\[ \frac{-8x^2}{-2x} + \frac{2x}{-2x} - \frac{1}{-2x} \][/tex]
Now, let's simplify each fraction individually:
1. Simplify [tex]\( \frac{-8x^2}{-2x} \)[/tex]:
[tex]\[
\frac{-8x^2}{-2x} = \frac{8x^2}{2x} = 4x
\][/tex]
(Because the negatives cancel each other out and [tex]\( 8x^2 \div 2x = 4x \)[/tex]).
2. Simplify [tex]\( \frac{2x}{-2x} \)[/tex]:
[tex]\[
\frac{2x}{-2x} = -1
\][/tex]
(Because [tex]\( \frac{2x}{2x} = 1 \)[/tex] and we have one negative sign).
3. Simplify [tex]\( \frac{-1}{-2x} \)[/tex]:
[tex]\[
\frac{-1}{-2x} = \frac{1}{2x}
\][/tex]
(Again, the negatives cancel each other out).
Finally, combine all the simplified parts together:
[tex]\[ 4x - 1 + \frac{1}{2x} \][/tex]
So, the simplified form of the given expression
[tex]\[ \frac{-8x^2 + 2x - 1}{-2x} \][/tex]
is:
[tex]\[ 4x - 1 + \frac{1}{2x} \][/tex]
This is the simplified expression.
