Explanation:
so, let's look at the options.
A. (x+3)/x = 3
that hurts already by just looking at it.
but let's check anyway :
x + 3 = 3x
3 = 2x
and that is only true for one value of x (3/2), but not in general.
so, this is wrong.
B. (x²+5)/5 = x² + 1
x² + 5 = 5x² + 5
x² = 5x²
that is only true for one value of x (0), but not in general.
so, this is wrong.
C. (2x+7)/(2x+9) = 7/9
9(2x+7) = 7(2x+9)
18x + 63 = 14x + 63
4x = 0
that is only true for one value of x (0), but not in general.
so, this is wrong.
D. (-5x - 10)/(x+2) = -5
-5x - 10 = -5(x + 2) = -5x - 10
now this is true in all cases, so this is correct.
make simple :
(a² - 4a + 4) / (a² - 4)
with a little bit of experience you see right away that
a² - 4a + 4 = (a - 2)²
as we know from the generic squaring
(a - b)² = a² - 2ab + b² : a perfect fit.
and
(a² - 4) = (a + 2)(a - 2)
as we know from the generic factor multiplying
(a+b)(a-b) = a² + ab - ab - b² = a² - b² : a perfect fit.
so, the given expression is actually
(a - 2)² / ((a - 2)(a + 2)) = ((a-2)(a-2)) / ((a-2)(a+2))
and so, after eliminating one (a-2) term in the numerator and in the denominator the following remains :
(a - 2) / (a + 2)
and that is answer A