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Multiply and simplify please

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3 Answers

Multiplying the fractions results in:

f(x)=(x^2-2x-48)(9x^3-4x)/((3x^3-2x^2)(8x-64))

f(x)=x(x-8)(x+6)(9x^2-4)/(8x^2(3x-2)(x-8))

9x^2-4 = (3x)^2-2^2 = (3x+2)(3x–2)

f(x)=x(x-8)(x+6)(3x+2)(3x–2)/(8x^2(3x-2)(x-8))

f(x)=x(x-8)(3x–2)/(x(x-8)(3x–2))
* (x+6)(3x+2)/(8x)

x(x-8)(3x–2)/(x(x-8)(3x–2))
= {1 if x ≠ 0, 2/3, or 8; UNDEFINED otherwise }
I.e., there are “Holes” at x = 0, 2/3, or 8.

f(x)=(x+6)(3x+2)/(8x), x ≠ 0, 2/3, or 8
 
Since x is in the denominator of this reduced form there will be a vertical asymptote at x = 0.
 
f(x)=(3x^2+20x+12)/(8x), x ≠ 0, 2/3, or 8
 
Do long division of numerator by denominator:
 
3x^2+20x+12 | 3x/8
3x^2
––––––––––––
20x+12 | 20/8
20x
––––––
12
 
f(x)=3x/8 + 20/8 + 12/(8x), x ≠ 0, 2/3, or 8
 
f(x)=3x/8 + 5/2 + 3/(2x), x ≠ 0, 2/3, or 8
 
This is the simplest form; it shows a slant asymptote of y=3x/8 + 5/2.
Hi Theresa,
 
x²-2x-48=x²-8x+6x-48
 
              =x(x-8)+6(x-8)
             =(x+6)(x-8)
 
3x³-2x²=x²(3x-2)
 
9x³-4x=x(9x²-4)
 
          =x(3x-2)(3x+2)
 
8x-64=8(x-8)
 
so the given expression becomes,
 
(x+6)(x-8) × (x)(3x-2)(3x+2)
x²(3x-2)         8(x-8)
 
(x+6)(3x+2)
    8x
 
For x=-6,-2/3 and 0 the solution is not defined.
Hi Theresa,
 
factors of
x^2-2x-48=(x-8)(x+6)
3x^3-2x^2 = x^2(3x-2)
9x^3-4x = x(9x^2-4)= x(3x-2)(3x+2)
8x-64 = 8( x-8)
 
using all this factors,
(x-8)(x+6)  *  x(3x-2)(3x+2)
________      _____________
x^2(3x-2)      8(x-8)
 
=(x+6)(3x+2)
  __________
     8 x
 
=3x^2+20x+12
  ___________  
     8x                                     
 
 
Meena from Strongsville,OH