Question

Simplify please and add a step by step explanation thanks!

Answer 1

Answer:

  y = (x +7)/(x -7)

Step-by-step explanation:

For dividing fractions like this, you can use the relation ...

  $\dfrac{a}{b}\div\dfrac{c}{d}=\dfrac{a}{b}\times\dfrac{d}{c}=\dfrac{ad}{bc}$

The simplification is done by cancelling common factors from numerator and denominator. In order to do that, we need to factor the numerator and denominator. We see that factors of 2, (x-2), and (x+7) will cancel.

  $y=\dfrac{(2x^2+10x-28)(x+7)}{(x^2-49)(2x-4)}=\dfrac{2(x-2)(x+7)(x+7)}{2(x-2)(x+7)(x-7)}\\\\\boxed{y=\dfrac{x+7}{x-7}}$

Answer 2

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In order to simplify, by cross multiplication we can see that the factors of 2 i.e (x - 2) and (x + 7) will get cancelled.

$:\implies\sf{y = \frac{(2 {x}^{2} + 10x - 28)(x + 7) }{( {x}^{2} - 49)(2x - 4)} } \\ \\ \\ :\implies\sf{ y = \frac{2(x - 2)(x + 7)(x + 7)}{2(x - 2)(x + 7)(x - 7)} } \\ \\ \\ :\implies\sf{y = \frac{ x+ 7}{x - 7} }$