How do you graph #F(x)=((4x^2)+8x-32)/((2x^2)-6x+4)#?

1 Answer
hsk
Jul 8, 2015

factorize the numerator and denominator separately

Explanation:

#F(x) = (4x^2+8x-32)/(2x^2-6x+4)#

can be factorized using rules for quadratic equation to simplify equation

Step 1 Taking 4 common from numerator and 2 from denominator

#F(x) = (4(x^2+2x-8))/(2(x^2-3x+2))#

Step 2 factorizing numerator and denominator

#F(x) = (4(x^2+ **4x-2x** -8))/(2(x^2- **2x-x** +2))#

in this step i have changed the middle term in both numerator and denominator in such a manner when you multiply 4x-2x you get -8 the third term in the numerator and similarly when you multiply -2x-x you get 2 the third term in the denominator

so now taking out common terms

#F(x) = (4(x(x+ 4)+(-2)(x+4)))/(2(x(x- 2)+(-1)(x +2)))#

#F(x) = (4(x-2)(x+4))/(2(x-1)(x -2))#

#F(x) = (2(x+4))/((x-1)#

graph{(2(x+4))/((x-1) [-infinity, infinity]}

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