Answer:
- [tex]\frac{2}{3}[/tex] x
Step-by-step explanation:
Given
[tex]\frac{4x-8x^2}{12x-6}[/tex] ← factorise numerator and denominator
= [tex]\frac{4x(1-2x)}{6(2x-1)}[/tex] ← factor out - 1 from (1 - 2x) on numerator
= [tex]\frac{-4x(2x-1)}{6(2x-1)}[/tex] ← cancel the common factor (2x - 1)
= [tex]\frac{-4x}{6}[/tex] ← cancel 4 and 6 by 2
= - [tex]\frac{2}{3}[/tex] x
Simplifying the expression will give us: [tex]\frac{4x-8x^2}{12x-6} = \frac{-2x}{3}[/tex]
Given the expression, [tex]\frac{4x-8x^2}{12x-6}[/tex], we are required to simplify the expression as follows:
Step 1: Factorize the denominator and the numerator.
[tex]\frac{4x-8x^2}{12x-6}\\\\=\frac{(1 - 2x)4x}{(2x - 1)6}[/tex]
Step 2: Rewrite the fraction by factoring out -1 from the numerator.
[tex]=\frac{(2x - 1)-4x}{(2x - 1)6}[/tex]
Step 3: Divide the numerator and denominator by (2x - 1) respectively.
[tex]=\frac{-4x}{6}[/tex]
Step 4: Divide the numerator and denominator by 2 respectively.
[tex]=\frac{-2x}{3}[/tex]
Therefore, simplifying the expression will give us: [tex]\frac{4x-8x^2}{12x-6} = \frac{-2x}{3}[/tex]
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