Answer:
The answer is
[tex] \frac{ {x}^{2} + 2x}{2x - 4 } [/tex]
Step-by-step explanation:
[tex] \frac{7xy}{ {x}^{2} - 4x + 4 } \div \frac{14y}{x^{2} - 4} [/tex]
To simplify , factorize
x² - 4x + 4 and x² - 4
For x² - 4x + 4
Write - 4x as a difference
x² - 2x - 2x + 4
x( x - 2) - 2(x - 2)
(x - 2)(x - 2)
For x² - 4
use the formula
a² - b² = ( a+b)( a - b)
That's
x² - 4 = (x + 2)(x - 2)
So now we have
[tex] \frac{7xy}{(x - 2)(x - 2)} \div \frac{14y}{(x + 2)(x - 2)} [/tex]
Change the division sign to multiplication sign and reverse the second fraction
That's
[tex] \frac{7xy}{(x - 2)(x - 2)} \times \frac{(x + 2)(x - 2)}{14y} [/tex]
Simplify
We have
[tex] \frac{x}{(x - 2)(x - 2)} \times \frac{(x + 2)(x - 2)}{2} [/tex]
Reduce the expression with x + 2
That's
[tex] \frac{x}{x - 2} \times \frac{x + 2}{2} [/tex]
Multiply the fractions
[tex] \frac{x(x + 2)}{2(x - 2)} [/tex]
We have the final answer as
[tex] \frac{ {x}^{2} + 2x }{2x - 4} [/tex]
Hope this helps you
