Question

Simplify%20%20%2B%204x%20-%2016%7D%20" id="TexFormula1" title=" \frac{ {x}^{2} - 4x + 4}{2 {x}^{2} + 4x - 16} " alt=" \frac{ {x}^{2} - 4x + 4}{2 {x}^{2} + 4x - 16} " align="absmiddle" class="latex-formula">

Answer 1

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