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

Jul 8, 2015

factorize the numerator and denominator separately

#### Explanation:

$F \left(x\right) = \frac{4 {x}^{2} + 8 x - 32}{2 {x}^{2} - 6 x + 4}$

can be factorized using rules for quadratic equation to simplify equation

Step 1 Taking 4 common from numerator and 2 from denominator

$F \left(x\right) = \frac{4 \left({x}^{2} + 2 x - 8\right)}{2 \left({x}^{2} - 3 x + 2\right)}$

Step 2 factorizing numerator and denominator

$F \left(x\right) = \frac{4 \left({x}^{2} + \ast 4 x - 2 x \ast - 8\right)}{2 \left({x}^{2} - \ast 2 x - x \ast + 2\right)}$

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

$F \left(x\right) = \frac{4 \left(x \left(x + 4\right) + \left(- 2\right) \left(x + 4\right)\right)}{2 \left(x \left(x - 2\right) + \left(- 1\right) \left(x + 2\right)\right)}$

$F \left(x\right) = \frac{4 \left(x - 2\right) \left(x + 4\right)}{2 \left(x - 1\right) \left(x - 2\right)}$

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

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