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Verified answer

task/30185433 Упростите выражение  1/(1-2x) +1/(1+2x) +2/(1+4x²)+4/(1+16x⁴)

решение     * * *  всего :   ( a - b )*( a + b ) = a² - b²   * * *

1 / (1 - 2x) +1 / (1 + 2x) +2 / (1 + 4x²)+4 / (1 + 16x⁴)  =

( 1 + 2x + 1 - 2x ) / (1 - 2x)(1 + 2x ) + 2 / (1+4x²) + 4 / (1 + 16x⁴)  =

2 / (1 - 4x²)+ 2 / (1 + 4x²) + 4 / (1+16x⁴)  =

2(1 + 4x² + 1 - 4x²) / (1 - 4x²)(1 + 4x²) + 4 / (1+16x⁴) = 4 / (1 - 16x⁴) + 4 / (1+16x⁴) =

4 (1 + 16x⁴ + 1 - 16x⁴) / (1 - 16x⁴) (1+16x⁴)  = 8 / (1 - 256x⁸) .