Answer:
The detailed process of simplification is :
Step-by-step explanation:
[tex]\frac{24x^{5} - 8x^{4} + 12x^{3} - 4x^{2} }{4x^{2} }[/tex]
= [tex]\frac{24x^{5} }{4x^{2} }[/tex] - [tex]\frac{8x^{4} }{4x^{2} }[/tex] + [tex]\frac{12x^{3} }{4x^{2} }[/tex] - [tex]\frac{4x^{2} }{4x^{2} }[/tex] ..........................separate the terms
= 6[tex]x^{5-2}[/tex] - 2[tex]x^{4-2}[/tex] + 3[tex]x^{3-2}[/tex] - 1 ................ subtract the power of x from denominator
= 6[tex]x^{3}[/tex] - 2[tex]x^{2}[/tex] + 3[tex]x[/tex] -1
= 2[tex]x^{2}[/tex]( 3[tex]x[/tex] -1 ) + (3[tex]x[/tex] -1 )................................... Take (3[tex]x[/tex] -1 ) common in (6[tex]x^{3}[/tex] - 2[tex]x^{2}[/tex])
= (3[tex]x[/tex] -1 ) (2[tex]x^{2}[/tex] +1) .......................................Take (3[tex]x[/tex] -1 ) common in whole equation
