Question

Сократите дробь
1)
2x^2-2
________
3x^2+6x+3
2)
8-8t+2t^2
_________
12-3t^2

Answer 1

1) 
2x^2-2
________
3x^2+6x+3

Решение:

2(x^2-1) / 3(x^2 + 2x +1)

2(x-1)(x+1) / 3(x+1)^2

2(x-1) / 3(x+1)

2x - 2 / 3x + 3
------------------------------------------------------------------------------------------
2) 
8-8t+2t^2
_________
12-3t^2
Решение:

2(4-4t+4^2) / 3(4-t^2)

2(2-t)^2 / 3(2-t)(2+t)

2(2-t) / 3(2+t)

4-2t / 6+3t

Answer 2

1)
$\frac{2 x^{2} -2}{3 x^{2} +6x+3} = \frac{2( x^{2} -1)}{3( x^{2} +2x+1)} = \frac{2(x-1)(x+1)}{3( x+1)^{2} } = \frac{2(x-1)(x+1)}{3(x+1)(x+1)} = \frac{2(x-1)}{3(x+1)}$
2)
$\frac{8-8t+2t^2}{12-3t^2} = \frac{2(4-4t+t^2)}{3(4-t^2)} = \frac{2*(2-t)^2}{3*(2^2-t^2)} = \frac{2*(2-t)*(2-t)}{3*(2-t)(2+t)} = \frac{2(2-t)}{3(2+t)}$