Question

Simplify

Answer 1

Answer:

The answer is

$\frac{ {x}^{2} + 2x}{2x - 4 }$

Step-by-step explanation:

$\frac{7xy}{ {x}^{2} - 4x + 4 } \div \frac{14y}{x^{2} - 4}$

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

$\frac{7xy}{(x - 2)(x - 2)} \div \frac{14y}{(x + 2)(x - 2)}$

Change the division sign to multiplication sign and reverse the second fraction

That's

$\frac{7xy}{(x - 2)(x - 2)} \times \frac{(x + 2)(x - 2)}{14y}$

Simplify

We have

$\frac{x}{(x - 2)(x - 2)} \times \frac{(x + 2)(x - 2)}{2}$

Reduce the expression with x + 2

That's

$\frac{x}{x - 2} \times \frac{x + 2}{2}$

Multiply the fractions

$\frac{x(x + 2)}{2(x - 2)}$

We have the final answer as

$\frac{ {x}^{2} + 2x }{2x - 4}$

Hope this helps you