Question

A) a*3 + a --------- a*2 b) x*2 - 2x ----------- x*2-4

Answer 1

1) Выражения решены так, как они читаются :
$\frac{a*3 + a}{a * 2} = \frac{3a+a}{2a} = \frac{4a}{2a} = \frac{2}{1} = 2 \\ \\ \frac{x*2 - 2x }{x*2 - 4} = \frac{2x-2x}{2x-4} = \frac{0}{2x-4} = 0$

2) Если " *3 "  = 3 степени , "*2" = 2 степени
$\frac{a^3 + a}{a^2} = \frac{a(a^2 + 1)}{a*a} = \frac{a^2+1}{a} = \frac{a^2}{a} + \frac{1}{a} = a + \frac{1}{a} \\ \\ \frac{x^2-2x}{x^2-4} = \frac{x(x-2)}{x^2-2^2} = \frac{x(x-2)}{(x-2)(x+2)} = \frac{x}{x+2}$

Answer 2

To simplify the given expressions, let's start with each one:

A) a3 + a To simplify this expression, we can factor out the common term 'a' from both terms: a3 + a = a*(3 + 1) = a*4 = 4a

B) x2 - 2x x2 - 4 To simplify this expression, we need to factor both the numerator and the denominator: x2 - 2x can be factored as x(x - 2) x2 - 4 can be factored as (x + 2)(x - 2)

Now, we can cancel out the common factor (x - 2) from both the numerator and the denominator: (x*(x - 2)) / ((x + 2)*(x - 2))

Notice that (x - 2) is in both the numerator and the denominator. When a common factor appears in both places, it can be canceled out, leaving us with the simplified expression:

x / (x + 2)

So, the simplified expression for B) is x / (x + 2).