How do you simplify $\frac{5}{y - 2} = y + 2$ $5 / (y - 2)= y + 2$ ?

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Answer 1 · 2018-04-27T03:38:34

$y = \pm 3$ $y=+-3$

By transposing the terms and using simple algebra, we get-

5=(y+2)(y-2)
Using $a^{2} - b^{2} = (a + b) (a - b)$ $a^2-b^2=(a+b)(a-b)$ ,
5= $y^{2} - 4$ $y^2-4$
$y^{2} = 9$ $y^2=9$
$y = \pm 3$ $y=+-3$

Answer 2 · 2018-04-27T04:36:58

$y = \pm 3$ $y = +-3$

$\frac{5}{y - 2} = y + 2$ $5/(y-2) = y+2$

Multiply both sides by $y - 2$ $y-2$ :
$5/cancel((y-2)) cancel(color(red)(*(y-2))) = (y+2)color(red)((y-2))$

Simplify:
$5 = y^2 - 4$

Add $4$ on both sides of the equation:

$5 quadcolor(red)(+quad4) = y^2 - 4 quadcolor(red)(+quad4)$

$9 = y^2$

Therefore, $y = +-3$

( $+-$ refers to "plus or minus")

Hope this helps!

How do you simplify 5 / (y - 2)= y + 2 5y−2=y+25 / (y - 2)= y + 2 ?