Question

rozwiąz równanie:

1) 4 3

------------- = -------------

x+1 x-2

2) x 1 x+6

------------ + -------- = -----------

x+3 x+2 x2 +5x+6

Answer 1

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

3(x+1) = 4(x-2)

3x + 3 = 4x - 8

x = 11

 

x/(x+3) + 1/(x+2) = (x+6)/(x^{2}+5x+6)

[x(x+2) + 1(x+3)]/[(x+3)(x+2)] = (x+6)/(x^{2}+5x+6)

(x^{2}+2x+x+3)/(x^{2}+5x+6) = (x+6)/(x^{2}+5x+6)         /:(x^{2}+5x+6)   

x^{2}+3x+3 = x+6

x^{2}+2x-3=0

(x+3)(x-1) = 0

x = -3 lub x = 1