Q:

Simplify[tex] \frac{ {x}^{2} - 4x + 4}{2 {x}^{2} + 4x - 16} [/tex]

Accepted Solution

A:
The first step to solve this expression is to use a² - 2a b + b² = (a - b)² to factor the expression
[tex] \frac{(x - 2)^{2} }{2 x^{2} + 4x - 16} [/tex]
Factor out 2 from the expression
[tex] \frac{(x - 2)^{2} }{2( x^{2} + 2x - 8)} [/tex]
Write 2x as a difference
[tex] \frac{(x-2)^{2} }{2 (x^{2} + 4x - 2x - 8)} [/tex]
Factor out x from the expression
[tex] \frac{(x - 2)^{2} }{2(x X (x + 4) -2x - 8)} [/tex]
Factor out -2 from the expression
[tex] \frac{(x-2)^{2} }{2(xX(x+4)-2(x+4))} [/tex]
Factor out x + 4 from the expression
[tex] \frac{(x-2)^{2} }{2(x+4)X(x-2)} [/tex]
Reduce the fraction with x - 2
[tex] \frac{x-2}{2(x+4)} [/tex]
Finally,, distribute 2 through the parenthesis to find your answer
[tex] \frac{x-2}{2x+8} [/tex]
This means that the correct answer to your question is [tex] \frac{x-2}{2x+8} [/tex] .
Let me know if you have any further questions
:)